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The Spectral Geometry on the submanifold of (pseudo-) Euclidean space

Research Project

Project/Area Number 09640119
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionSAGA UNIVERSITY

Principal Investigator

ISHIKAWA Susumu  Differential Geometry, SAGA UNIVERSITY, Professor, 理工学部, 教授 (10039258)

Co-Investigator(Kenkyū-buntansha) YAMADA Kotaro  Constant Mean Curvature, Kumamoto Univ., Associate Professor, 教養部, 助教授 (10221657)
KAWAI Shigeo  Differential Operator, SAGA UNIVERSITY, Professor, 文化教育学部, 教授 (30186043)
SHIOHAMA Katsuhiro  Riemannian Geometry, SAGA UNIVERSITY, Professor, 理工学部, 教授 (20016059)
MACHIGASHIRA Yoshiroh  Alexandorov Space, Osaka Kyoiku Univ., Lecturer, 講師 (00253584)
CHENG Qing ming  Submanifold Theory, Jousai Univ., Associate Professor, 理学部, 助教授 (50274577)
KAMETANI Yukio  Topological Geometry, SAGA UNIVERSITY, Research Associate (70253581)
Project Period (FY) 1997 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 1999: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1998: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1997: ¥1,700,000 (Direct Cost: ¥1,700,000)
KeywordsFinite Type Submanifold / Biharmonic Submanifold / Harmonic Map / Psudo-Euclidean Geometry / Spacelike Submanifold / Minimal Submanifold / Conformal Geometry / 部分多様体 / 平均曲率一定曲面 / スペクトル幾可 / 共形幾可 / 指定ユークツカド幾可 / アレクサンドロウ空間 / スペクトル幾何 / アレクサンドロフ空間 / 平均曲率一定曲面(CFIC)
Research Abstract

We obtained 25 and more prints in this Project (See REFERENCES).
In 1997
1. We obtained some new results about the classification of biharmonic submanifold in psudo-Euclidean space. In detail,
(1) The classification problem of biharmonic curves in psudo-Euclidean space was completed.
(2) It was proved that the bihaemonic surfaces do not exist in 3 dimensional psudo-Euclidean space.
(3) Some classification theorems of biharmonic surfaces in 4 dimensional psudo-Euclidean space was obtained.
2. About the spacelike maximal submanifolds with some conditions for Ricci curvature immersed in de-Sitter sphere in psudo-Euclidean space, the classification of them was discussed.
3. About the hypersurfaces of constant scalar curvature immersed in de-Sitter sphere in psudo-Euclidean space, the sphere theorem was discussed.
4. About the comformally flat 3 dimensional Riemannian manifolds under some conditions for Ricci curvature and scalar curvature, the classification problem of them was discussed.
In 1998
1. … More We obtained, under some conditions for scalar curvature, that any compact submanifold immersed in de-Sitter sphere in psudo-Euclidean space is only a standard sphere.
2. We obtained a characterization about the Clifford torus.
3. (1) We discussed about 3-dimensional comformally flat Riemannian manifold with non negative constant scalar curvature and the constan norm of Ricci curvature.
(2) We discussed about 3-dimensional comformally flat Riemnnian manifold with negative constant scalar curvature and the constan norm of Ricci curvature.
In 1999
1. We discussed the classification problem about the minimal closed surfaces in unit sphere with bounded norm of Ricci curvature. This result is concerted with the famous theorem by S.S.Chern, do Carmo and S. Kobayashi that the Clifford torus is only minimal closed surfaces of S=n in unit sphere.
2. We obtained some progress concerned with the third work of listed in 1998
3. We now investigate the following open problems proposed by Bang-yen Chen;
(1) The classification problem of the finite type surface in 3 Euclidean space.
(2) The classification problem of the biharmonic submanifolds in n-dimensional Euclidean space.
(3) The classification problem of the biharmonic submanifolds in 4-dimensional Minkovski space. Less

Report

(4 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • 1997 Annual Research Report
  • Research Products

    (93 results)

All Other

All Publications (93 results)

  • [Publications] Qing-Ming Cheng and Susumu Ishikawa: "Complete maximal spacelike submanifolds"Kodai Mathmatical Journal. Vol. 20. 208-217 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng and Katsuhiro Shiohama: "Non-Existence of Stable currents II"Kyushu Journal of Mathmatics. Vol. 51. 149-164 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Katsuhiro Shiohama and Hongwei Xu: "Lower bound for L^<n/2> curvature norm and its application"The Journal of Geometric Analysis. Vol. 7. 377-386 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Katsuhiro Shiohama and Hongwei Xu: "The topological sphere theorem for complete submanifolds"Compositio Mathematica. Vol. 107. 221-232 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masaaki Umehara and Kotaro Yamada: "Geometry of surfaces of constant mean curvature 1 in the hyperbolic 3-space"Sugaku Expositions (translated by the authors from Japanese). Vol. 10. 41-55 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masaaki Umehara and Kotaro Yamada: "A duality on CMC-1 surface in the hyperbolic 3-space and a hyperbolic analogue of the Osserman Inequality"Tsukuba Journal of mathmatics. Vol. 21. 229-237 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Wayne Rossman, Masaaki Umehara and Kotaro Yamada: "Irreducible constant mean curvature 1 surfaces in hyperbolic space with positive genus"Tohoku Mathematical journal. Vol. 49. 449-484 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Bang-Yen Chen and Susumu Ishikawa: "Biharmonic Pseudo-riemannian submanifolds in pseudo-Euclidean spaces"Kyushu Journal of Mathematics. Vol. 52. 167-185 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng and Susumu Ishikawa: "Spacelike hypersurfaces with constant scalar curvature"Manuscripta Mathematics. Vol. 95. 499-505 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hongcang Yang and Qing-Ming Cheng: "chern7s conjecture on minimal hypersurfaces"Mathematische Zeitschrift. Vol. 227. 377-390 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng, Yoshiroh Machigashira and Yoshihiro Sugioka: "The relation between degree and dilatation of continuous maps"Japanese Journal of Mathematics. Vol. 24. 183-190 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yoshiroh Machigashira: "the Gaussian Curvature of Alexanfrov surfaces"Journal of Mathematical Sciety of Japan. Vol. 50. 859-878 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Katsuhiro Shiohama and Hongwei Xu: "A general rigidity theorem for complete submanifolds"Nagoya Mathematical Journal. Vol. 150. 105-134 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng, Susumu Ishikawa and katsuhiro Shiohama: "Confarmally flat 3-manifolds with constant scalr curvature"Journal of Mathematical Socuety of Japan. Vol. 51. 209-226 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng, Susumu Ishikawa: "A characterization of the Clifford torus"Proceeding of the American Mathematical Society. Vol. 127. 819-828 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Wayne Rossman, masaaki Umehara and Kotaro Yamada: "Flux for mean cyrvature 1 surfaces in hyperbolic 3-space, and applications"Proceedings of the American mathematical Society. Vol. 127. 2147-2154 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Shigeo Kawai: "p-Harmonic Maps and convex Functions"Geometriae Dedicata. Vol. 74. 261-265 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Shigeo Kawai, Nobumitsu nakauchi and hiroshi takeuchi: "on the Existence of n-Harmonic Spheres"Composiotio Mathematica. Vol. 117. 33-43 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Katsuhiro Shiohama: "Sphere Theorems"Handbook of Differential Geometry (Edited by G.Dillen and P.Verstraelen). Vol. 1 Chapter 8. 867-903 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Katsuhiro Shiohama and Hongwei Xu: "Rigidity and sphere theorems for submanifolds II"Kyushu Journal of Mathematics. Vol. 54. 103-109 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] shin Kato, Masaaki umehara and Kotaro Yamada: "Genaral existence of minimal surfaces of genus zero with catenoidal ends and prescribed flux"Communications in Analysis and Geometry. Vol. 8. 83-114 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masaaki Umehara and Kotaro Yamada: "Metrics of constant curvature 1 with three conical singularities on 2-sphere"Illinois Journal of mathematics. (to appear). (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng, Susumu Ishikawa and Katsuhiro Shiohama: "Conformally flat 3-manifolds with constant scalar curvature II"Japanese Journal of Mathematics. (to appear). (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng: "Compact locally conformally flat Reimannian manifolds"(preprint).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng: "Compact and Noncompact hypersurfaces in a space form M^<n+1>(c) with constant mean curvature"(preprint).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masaaki Umehara and Kotaro Yamada: "Metrics of constant curvature 1 with three conical singularities on 2-sphere"Inidiana Journal of Mathematics. 1999.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Kazuhiro Kuwae, Yoshiroh Machigashira and Takashi Shioya: "Sobolev spaces. laplacian, and Heat Kernel on Alexandrov spaces"(preprint).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng and Katsuhiro Shiohama: "Nonexistence of integral currents II"Kyushu Journal of Mathematics. Vol. 51. 149-164 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Shin Kato, Masaaki Umehara and Kotaro Yamada: "An inverse problem of the flux formula"Proceedings of the 4th International Congress of Geometry (Thessaloniki, 19, Giachoudis-Giapoulis, Thessaloniki. 228-233 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng and Susumu Ishikawa: "Complete maximal spacelike Submanifolds"Kodai Mathematical Journal. 20. 208-217 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng and Katsuhiro Shiohama: "Non-Existence of Stable currents II"Kyushu Mathematical Journal. 51. 149-164 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Katsuhiro Shiohama and Hongwei Xu: "Lower bound for L-D1n/2-|D1 curvature norm and its application"The Journal of Geometric Analysis. 7. 377-386 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Katsuhiro Shiohama and Hongwei Xu: "The topological sphere theorem for complete submanifolds"Compositio Mathematica. 107. 221-232 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masaaki Umehara and Kotaro Yamada: "Geometry of surface of constant mean curvature 1 in the hyperbolic 3-space"Sugaku Expositions. 10 (translated by the authors from Japanese). 41-55 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masaaki Umehara and Kotaro Yamada: "A duality on CMC-1 surface in the hyperbolic 3-space and a hyperbolic analogue of the Osserman Inequality"Tsukuba Journal of Mathematics. 21. 229-237 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Wayne Rossman, Masaaki Umehara and Kotaro Yamada: "Irreducible constant mean curvature 1 surface in hyperbolic space with positive genus"Tohoku Mathematical Journal. 49. 449-484 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Bang-Yen Chen and Susunmu Ishikawa: "Biharmonic Pseudo-Riemannian submanifolds in Pseudo-Euclidean spaces"Kyushu Journal of Mathematics. 52. 167-185 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng and Susumu Ishikawa: "Spacelike hypersurfaces with constant scalar curvature"Manuscripta Mathematics. 95. 499-505 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hongcang Yang and Qing-Ming Cheng: "Chern's conjecture on minimal hypersurfaces"Mathematische Zeitschrift. 227. 377-390 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng, Yoshiroh Machigashira and Yoshihiro Sugioka: "The relation between degree and dilatation of continuous maps"Japanese Journal of Mathematics. 24. 183-190 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yoshiroh Machigashira: "The Gaussian Curvature of Alexandrov surfaces"Journal of Mathematical Society of Japan. 50. 859-878 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Katsuhiro Shiohama and Hongwei Xu: "A general rigidity theorem for complete submanifolds"Nagoya Mathematical Journal. 150. 105-134 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng, Susumu Ishikawa and Katsuhiro Shiohama: "Conformally flat 3-manifolds with constant scalar curvature"Journal of Mathematical Society of Japan. 51. 209-226 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng, Susumu Ishikawa: "A characterization of the Clifford torus"Proceeding of American Mathematical Society. 127. 819-828 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Wayne Rossman, Masaaki Umehara and Kotaro Yamada: "Flux for mean curvature 1 surfaces in hyperbolic 3-space, and applications"Proceeding of American Mathematical Society. 127. 2147-2154 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Shigeo Kawai: "p-Harmonic Maps and Convex Functions"Geometriae Dedicata. 74. 261-265 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Shigeo Kawai, Nobumitsu Nakauchi and Hiroshi Takeuchi: "On the Existence of n-Harmonic Spheres"Compositio Mathematica. 117. 33-43 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Katsuhiro Shiohama: "Sphere Theorems"Handbook of Differential Geometry (Edited by G.Dillen and P.Verstraelen). 1 chapter 8. 867-903 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Katsuhiro Shiohama and Hongwei Xu: "Rigidity and sphere theorems for submanifolds II"Kyushu Journal of Mathematics. 54. 103-109 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Shin Kato, Masaaki Umehara and Kotaro Yamada: "General existence of minimal surfaces of genus zero with catenoidal ends and prescribed flux"Communications in Analysis and Geometry. 8. 83-114 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masaaki Umehara and Kotaro Yamada: "Metrics of constant curvature 1 with three conical singularities on 2-sphere"to appear in Illinois Journal of Mathematics.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng, Susumu Ishikawa and Katsuhiro Shiohama: "Conformally flat 3-manifolds with constant scalar curvature II"to appear Japanese Journal of Mathematics. 26. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng: "Compact locally conformally flat Riemannian manifolds"Preprint.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng: "Compact and Noncompact hypersurfaces in a space form M|-D1n+1-|D1(c) with constant mean curvature"preprint.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Qing-Ming Cheng: "A Characterization of the Clifford torus"Proc.Amer.Math.Soc.. 127. 819-828 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Qing-Ming Cheng: "Conformally flat 3-manifolds with constant・・・"Jour.Math.Soc.Japan. 51. 209-226 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Qing-Ming Cheng: "Conformally flat 3-manifolds with・・・II"To appear in Japanese J.Math.. 26. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] Qing-Ming Cheng: "Complete maximal spacelike surfaces・・・"To appear in Glasgow Math.J.. 42. 139-156 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] Katsuhiro Shiohama: "Rigidity and sphere theorems for submanifold"To appear in Kyushu Jour.Math..

    • Related Report
      1999 Annual Research Report
  • [Publications] Shigeo Kawai: "p-harmonic maps and convex functions"Geometriae Dedicata. 74. 261-265 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Shigeo Kawai: "On the existence of n-harmonic・・・"Compositio Mathematica. 117. 33-43 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Masaaki Umehara: "Metrics of constant curvature 1・・・"To appear in Illinois J.of Math..

    • Related Report
      1999 Annual Research Report
  • [Publications] Shin Kato: "General existence of minimal surfaces・・・"To appear in Comm.in Analysis and Gemetry.

    • Related Report
      1999 Annual Research Report
  • [Publications] Wayne Rossman: "A new flux for mean curvature 1・・・"Proceedings of A.M.S. 127. 2147-2154 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Kazuyoshi Kuwae: "Sobolev spaces,Laplacian,and Heat・・・"To appear in Math.Z..

    • Related Report
      1999 Annual Research Report
  • [Publications] Kazuyoshi Kuwae: "Beginning of analysis on Alexandrov spaces"To appear in Prceed.Conf.on Geom and Top..

    • Related Report
      1999 Annual Research Report
  • [Publications] Qing-Ming Cheng.: "The relation between degree anddilatation of continnous maps" Japanese Journal of Mathematics. 24・1. 183-190 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Hongcang Yang: "Chern's conjecture on minimal hypersurfaces" Mathematrische Zeitschrift. 227. 377-390 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Qing-Ming Cheng: "Spacelike hypersurfaces with constant scalar curvature" Manuscipta Mathematics. 95. 499-505 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Qing-Ming Cheng: "A characterization of the Clifford torus" Proceeding of American Mathematical Society. 127. 819-828 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Qing-Ming Cheng: "Conformally flat 3-manifolds with constant scalar curvature" Journal of Mathematical Society of Japan. 51. 207-226 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Katsuhiro Shiohama: "Recent topics in the geometry of Alexanoo spaces" Proc.Intern.Daewoo Workshop. 16・3. 21-34 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] Katsuhiro Shiohama: "A general rigidity theorem for complete submanifolds" Nagoya Mathematical Journal. 150. 105-134 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Katsuhiro Shiohama: "Lower bound for L^<n/2> curature norm and its application" to appear in the Journal of Geometric Analysis. 8. (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Umehara: "Metrics of constant curvature 1with three conical singularities on 2-sphere" To appear in Inidiana Journal of Mathematics. (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] W.Rossman: "A new flux for mean curvature 1surfaces in hyperbolic 3-space and applications" To appear in Proceedings of American Mathematical Society. (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Kawai: "On the existence of n-harmonic spheres" to appear in Compositio Mathematica.

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Kawai: "p-harmonic maps and convex functions" to appear in Geometriae Dedecata.

    • Related Report
      1998 Annual Research Report
  • [Publications] 河合茂生: "p-調和写像と凸関数" 第45回幾何学シンポジウム講演要旨. 323-328 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Machigashira: "The Gaussian curvature of Alexandrov surfaces" Journal of Mathematical Society of Japan. 50・4. 859-878 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Kuwae: "Begining of Analysis on Alexandrou Spaces" Kyushu Univ.Preprint Sevies in Math. 36. 1-11 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Bang-Yen Chen: "Biharmonic pseudo-Riemmannian submanifolds in pseudo-Eucidean spaces" Kyushu Journal of Mathematics. 52・1. 167-185 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] Qing-Ming Cheng: "Complete Maximal Spacelike Submanifolds" Kodai Mathematical Journal. 20・3. 208-217 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Qing-Ming Cheng: "Conformally flat3-manifolda with constant scalar curvature" Journal of the Mathematical Society of Japan. 51・1. (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] Qing-Ming Cheng: "Spacelike hyperswfaces with constant scalar cuwature" Manuscripta Mathematics. 95. (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] Qing-Ming Cheng: "Chern's conjecture on minimal hypersurfaces" Mathematische Zeitschrift. (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] Qing-Ming Cheng: "Non-existence of stable currents II" Kyushu Journal of Mathematics. 52. 149-164 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Shigeo Kawai: "On the existence of n-harmonic spheres" Compositio Mathematicae.

    • Related Report
      1997 Annual Research Report
  • [Publications] Shigeo Kawai: "P-harmonic maps and convex functions" Geometriae Dedicata.

    • Related Report
      1997 Annual Research Report
  • [Publications] Yoshiro Machigashira: "The Gaussian curvature of Alexandrov surfaces" Journal of the Mathematical Society of Japan.

    • Related Report
      1997 Annual Research Report
  • [Publications] Wayne Rossman: "A new flux for mean curvature I surfaces in hyperbolic 3-space" Proceedings of the American Mathematical Society.

    • Related Report
      1997 Annual Research Report
  • [Publications] Wayne Rossman: "Irreducible constant mean curvature 1 surfaces in hyperbolic space" Tohoku Mathematical Journal. 49. 449-484 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Shin Kato: "An inverse problem of the flux for minimal surfaces" Indiana University Mathematics Journal. 46. 529-560 (1977)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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