1997 Fiscal Year Annual Research Report

多様体に関する数理科学的諸問題

Research Project

Project/Area Number	07404001
Research Institution	Tohoku University
Principal Investigator	小田忠雄東北大学, 大学院・理学研究科, 教授 (60022555)
Co-Investigator(Kenkyū-buntansha)	新井仁之東北大学, 大学院・理学研究科, 教授 (10175953) 坂東重稔東北大学, 大学院・理学研究科, 教授 (40165064) 石田正典東北大学, 大学院・理学研究科, 教授 (30124548) 西川青季東北大学, 大学院・理学研究科, 教授 (60004488) 森田康夫東北大学, 大学院・理学研究科, 教授 (20011653)
Keywords	トーリック多様体 / ミンコフスキー和 / アーベル多様体 / リーマン多様体 / ケーラー多様体 / 複素数多様体 / 微分作用素 / 非線型微分方程式
Research Abstract	本研究の目的および実施計画に沿って,多様体に関する諸問題を総合的見地から次のように研究した. 1.トーリック多様体の研究,特に整凸多面体の格子点,ミンコフスキー和,交差コホモロジー等の研究を行い,いくつかの新知見を得た. 2.久賀・佐武のアーベル多様体,有限体上の形式群等の数論的研究を行った. 3.負曲率等質リーマン多様体の間の調和写像の無限遠境界値問題,共形平坦多様体の変形を研究した. 4.ケーラー多様体のアインシュタイン・ケーラー計量の存在および安定性の研究を行った. 5.複素多様体の調和解析的研究を行った. 6.擬微分作用素,極大作用素,有界線形作用素,作用素環等の調和解析的・関数解析的研究を行った. 7.可換差分方程式系とラックス作用素との関係,ファインマン経路積分,電気伝導度の数理物理学的研究を行った. 8.多様体上における反応拡散方程式系,熱方程式,ナヴィア・ストークス方程式,スカラーフィールド方程式等の非線型微分方程式の研究を行った. 9.正標数およびp進体上の代数多様体の基本群を研究した.

Research Products

(18 results)

All Other

All Publications (18 results)

[Publications] Yasuo MORITA: "Remarks on a conjecture of Batyrev and Manin" Tohoku Math.J.49. 437-448 (1997)
[Publications] Seiki NISHIKAWA and K.UENO: "Dirichlet problem at iufinity for harmonic maps between Carrot spsces" Proc. Japan Acad. Ser.A. 73. 168-169 (1997)
[Publications] Masanori ISHIDA and F.KATO: "The Strong rigidity theorem for nonarchimedeau unifor mization" Tohoku Math.J.(出版予定). (1998)
[Publications] Shigetoshi BANDO: "The existeuce theorem of harnonui objects via Green function" Pnoc.of the Pacific Rim Geometry Conf.(発表予定). (1998)
[Publications] Hitoshi ARAI: "Generalized Dirichlit growth theorev and applications to ∂_Δ and hyperbolic equations" Coww. in Partial Differeutiol Equations. (発表予定). (1998)
[Publications] Kazuya TACHIZAWA and R.ROCHBERG: "Psem do differentiol sperators,Gabor frawes,and local trigonometvi basos" Gabor analysis and algorithws. 171-192 (1998)
[Publications] K0ji HASEGAWA: "Ruijsenaars′ commuting differeuce operators" Comm.Mash.Phys.187. 289-325 (1997)
[Publications] Yasuhiro NAKAGAWA: "Combinatorial for mulae for Futaki characters and geweralised Killing forws on torei FANO asbifolds" Proc.of the Pacific Rim Geomltry Conf.(発表予定). (1998)
[Publications] Satoru IGARI: "The Kakeya maximal operator with a special base" Approx.Thesny and Appl.13. 1-7 (1997)
[Publications] Kazuyuki TANAKA: "The self-embdding theorem of WKLO and a non-Standard method" Ann.Purl and Appl.Logri. 84. 41-50 (1997)
[Publications] Takashi YOSHINO: "A siwple proof of Sarason′s result for interpolation in H" Yokohama Mash.J.44. 21-24 (1997)
[Publications] Tetsuo NAKAMURA: "On characteristic polynomials of formal groups over finite fields" Mash.Nachr.188. 289-299 (1997)
[Publications] Takeyuki NAGASAWA: "Navier-Stokes flow on Riemannian manifolds" Nonliear Aual.30. 825-832 (1997)
[Publications] Kazuyuki SAITO: "On σ-normal C^オ-algebras" Bull.London Mash.Soc.29. 480-482 (1997)
[Publications] Hiroyasu IZEKI: "The Teichmiiller distance on the space of flat conforwad stnuchires" Conforw.Geom.Dynam.2. 1-24 (1998)
[Publications] Setsuro FUJIIE: "Semiclassical represention of the scatlering matrix by a." Comm.Mash.Phoys.(発表予定). (1998)
[Publications] Fumihiko NAKANO: "Calculation of the Hall conductivity by zdiabatic approyimation" J.Mash.Si.,Uio.Tokyo. 4. 351-371 (1997)
[Publications] Kazuhiko HORIHATA: "Weak soluitions of harmomi mappingo on a bounded Minkowski opace-time noish imtial-boundary condifions." Comm.Partial liff.Equatius. (発表予定). (1998)

1997 Fiscal Year Annual Research Report

多様体に関する数理科学的諸問題

Principal Investigator

小田 忠雄 東北大学, 大学院・理学研究科, 教授 (60022555)

Research Products

[Publications] Yasuo MORITA: "Remarks on a conjecture of Batyrev and Manin" Tohoku Math.J.49. 437-448 (1997)

[Publications] Seiki NISHIKAWA and K.UENO: "Dirichlet problem at iufinity for harmonic maps between Carrot spsces" Proc. Japan Acad. Ser.A. 73. 168-169 (1997)

[Publications] Masanori ISHIDA and F.KATO: "The Strong rigidity theorem for nonarchimedeau unifor mization" Tohoku Math.J.(出版予定). (1998)

[Publications] Shigetoshi BANDO: "The existeuce theorem of harnonui objects via Green function" Pnoc.of the Pacific Rim Geometry Conf.(発表予定). (1998)

[Publications] Hitoshi ARAI: "Generalized Dirichlit growth theorev and applications to ∂_Δ and hyperbolic equations" Coww. in Partial Differeutiol Equations. (発表予定). (1998)

[Publications] Kazuya TACHIZAWA and R.ROCHBERG: "Psem do differentiol sperators,Gabor frawes,and local trigonometvi basos" Gabor analysis and algorithws. 171-192 (1998)

[Publications] K0ji HASEGAWA: "Ruijsenaars′ commuting differeuce operators" Comm.Mash.Phys.187. 289-325 (1997)

[Publications] Yasuhiro NAKAGAWA: "Combinatorial for mulae for Futaki characters and geweralised Killing forws on torei FANO asbifolds" Proc.of the Pacific Rim Geomltry Conf.(発表予定). (1998)

[Publications] Satoru IGARI: "The Kakeya maximal operator with a special base" Approx.Thesny and Appl.13. 1-7 (1997)

[Publications] Kazuyuki TANAKA: "The self-embdding theorem of WKLO and a non-Standard method" Ann.Purl and Appl.Logri. 84. 41-50 (1997)

[Publications] Takashi YOSHINO: "A siwple proof of Sarason′s result for interpolation in H" Yokohama Mash.J.44. 21-24 (1997)

[Publications] Tetsuo NAKAMURA: "On characteristic polynomials of formal groups over finite fields" Mash.Nachr.188. 289-299 (1997)

[Publications] Takeyuki NAGASAWA: "Navier-Stokes flow on Riemannian manifolds" Nonliear Aual.30. 825-832 (1997)

[Publications] Kazuyuki SAITO: "On σ-normal C^オ-algebras" Bull.London Mash.Soc.29. 480-482 (1997)

[Publications] Hiroyasu IZEKI: "The Teichmiiller distance on the space of flat conforwad stnuchires" Conforw.Geom.Dynam.2. 1-24 (1998)

[Publications] Setsuro FUJIIE: "Semiclassical represention of the scatlering matrix by a." Comm.Mash.Phoys.(発表予定). (1998)

[Publications] Fumihiko NAKANO: "Calculation of the Hall conductivity by zdiabatic approyimation" J.Mash.Si.,Uio.Tokyo. 4. 351-371 (1997)

[Publications] Kazuhiko HORIHATA: "Weak soluitions of harmomi mappingo on a bounded Minkowski opace-time noish imtial-boundary condifions." Comm.Partial liff.Equatius. (発表予定). (1998)

小田忠雄東北大学, 大学院・理学研究科, 教授 (60022555)