1998 Fiscal Year Annual Research Report

幾何学的複素解析

Research Project

Project/Area Number	09304014
Research Category	Grant-in-Aid for Scientific Research (A)
Research Institution	The University of Tokyo
Principal Investigator	野口潤次郎東京大学, 大学院・数理科学研究科, 教授 (20033920)
Co-Investigator(Kenkyū-buntansha)	志賀啓成東京工業大学, 大学院・理工学研究科, 助教授 (10154189) 辻元東京工業大学, 大学院・理工学研究科, 助教授 (30172000) 満渕俊樹大阪大学, 大学院・理学研究科, 教授 (80116102) 大沢健夫名古屋大学, 大学院・多元数理科学研究科, 教授 (30115802) 藤本坦孝金沢大学, 理学部, 教授 (60023595)
Keywords	多変数複素解析 / 幾何学的複素解析 / 小林双曲的多様体 / 値分布 / 不変計量 / モジュライ理論 / 擬凸領域 / タイヒミューラー空間
Research Abstract	大沢健夫(名大多元数理)は、C^2級の境界を持つ擬凸領域の研究を行い、Bergman計量のある評価式を得た。神本丈(熊本大)は、弱擬凸領域のべルグマン、ゼーゲー核の特異性、漸近展開の研究をした。山口博史(滋賀大)は、米谷氏(京都工繊大)と共同で、リーマン面上のべルグマン計量の変形を調べ調べ、それを多変数関数論に応用した。真次康夫(信州大)は、2次元トーラス上の2乗可積分空間の研究をした。神保敏弥(奈良教育大)は、Salagean作用素による関数D^<j-1>f(z)がp-Hardy空間に属する十分条件を与えた。吉田守(福岡大)は、ε-ノルムに関連する双一次形式の式ある評価式の詳細な証明を付けた.加藤満生(琉球大)は1変及び多変数超幾何微分方程式のモノドロミー群が有限既約になる条件を得た。奥間智弘(群馬工専)は、2次元複素解析空間の正規特異点の多重種数について成果を得た。高山茂晴(大阪大学)は、準アーベル多様体に対するLefschetz型定理を証明した。小林亮一(名大多元数理)は、完備リッチ平坦ケーラー計量の存在、退化、応用について研究した。森正気(山形大)は、与えられた超越的正則曲線の小変形で除外値なしに出来ることを示した。辻元(東工大)は、解析的ザリスキ分解の研究を行い、満淵俊樹(大阪大)と多重種数の変形不変性の研究で大きな進展をみた。志賀啓成(東工大)は、力学系の極限集合とジュリア集合の類似性を明らかにし、発散型双曲多様体上の正則写像の剛性と有限性についての条件を求めた.相原義弘(沼津工専)は、射影的代数多様体Mに値を持つ有理型写像の一意性定理を証明した。藤本坦孝(金沢大)は、複素射影空間への有理型写像の一意性定理について新しい結果を得た。若林功(成溪大)は、3,4次のThue不等式の整数解をPade近似の方法で求めた.野口潤次郎(代表者)は、正則写像の値分布、関数体上の値分布、代数多様体の有理点分布について研究し、正則曲線のLangの予想を準アーベル多様体に対し証明した。また当研究課題のとりまとめをした。

Research Products

(29 results)

All Other

All Publications (29 results)

[Publications] Y.Aihara: "Finiteness theorems for meromorphic mappings" Osaka J.Math.35. 593-618 (1998)
[Publications] H.Fujimoto: "Uniqueness problem with truncated multiplicities in value distribution theory" Nagoya Math.J.152. 1-21 (1998)
[Publications] H.Fujimoto: "Uniqueness problem with truncated multiplicities in value distribution theory II" to appear in Nagoya Math.J.
[Publications] Y.Itokawa and R.Kobayashi: "Minimizing currents in open manifolds and the n-1 homology of nonnegatively Ricci curved manifolds" to appear in Amer.J.Math.
[Publications] T.Jimbo and A.Sakai: "Polynomially convex hulls of graphs on the sphere" to appear in Proc.Amer.Math.Soc.
[Publications] J.Kamimoto: "Singularities of the Bergman kernel for certain weakly pseudoconvex domains" J.Math.Scie.Univ.Tokyo. 5. 99-117 (1998)
[Publications] J.Kamimoto: "Asympotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in C^2" Ann.Faculte Scie.Toulouse. 6. 51-86 (1998)
[Publications] J.Kamimoto: "On an integral of Hardy and Littlewood" Kyushu J.Math.52. 249-263 (1998)
[Publications] J.Kamimoto: "The Bergman kernel on certain decoupled domains" to appear in Proc.ISAAC Congress Reproducing Kernels and Their Applications,Kluwer Acad.Publ.
[Publications] J.Kamimoto: "On the multiplicities of the zeros of Laguerre-Polya functions" to appear in Proc.Amer.Math.Sco.
[Publications] J.Kamimoto: "On the singularities of non-analytic Szego kernels" to appear in J.Math.Scie.Univ.Tokyo.
[Publications] J.Kamimoto: "Remarks on Bloch functions on weakly pseudoconvex domains" 京都大学数理解析研究所講究録「再生核の理論とその応用」. 1067. 83-88 (1998)
[Publications] J.Kamimoto: "On an approximation on L^1(R^n)" 京都大学数理解析研究所講究録. (掲載予定).
[Publications] M.Kato: "Schwarz maps of _3F_2 with finite irreducible monodromy groups" Kyushu J.Math.52. 475-495 (1998)
[Publications] S.Mori: "Elimination of defects of meromorphic mappings of C^m into P^n(C)" to appear in Annal.Acad.Scie.Fennicae.Math.23. (1998)
[Publications] N.Niwa,T.Jimbo and S.Owa: "Hardy class of functions defined by the Salagean operator" Annal.Polonici Math.69. 25-30 (1998)
[Publications] J.Noguchi: "On holomorphic curves in semi-Abelian varieties" Math.Z.228. 713-721 (1998)
[Publications] J.Noguchi: "Value distribution theory of holomorphic mappings" Contemp.Math.Amer.Math.Soc.222. 109-129 (1999)
[Publications] T.Okuma: "The second pluri-genus of surface singularities" Compo.Math.110. 263-276 (1998)
[Publications] T.Okuma: "The pluri-genera of surface singularities" Tohoku Math.J.50. 119-132 (1998)
[Publications] T.Okuma: "The plurigenera of Gorenstein surface singularities" Manuscripta Math.94. 187-194 (1997)
[Publications] S.Saitoh and M.Yamamoto: "Intergral transforms involving smooth functions" to appear in Reproducing Kernels and Their Applications,Kluwer Academic Publishers,Boston.
[Publications] S.Saitoh: "Applications of the general theory of reproducing kernels" to appear in Reproducing Kernels and Their Applications,Kluwer Academic Publishers,Boston.
[Publications] S.Saitoh: "Nonlinear transforms and analyticity of functions" to appear in Nonlinear Mathematical Analysis and its Applications Halronic Press.Inc.,Florida,USA.
[Publications] S.Takayama: "Adjoint linear series on weakly 1-complete Kahler manifolds I: Global projective embedding" Math.Ann.311. 501-531 (1998)
[Publications] S.Takayama: "Adjoint linear series on weakly 1-complete kahler manifolds II: Lefschetz type theorem on quasi-Abelian varieties" Math.Ann.312. 363-385 (1998)
[Publications] H.Yamaguchi and F.Maitani: "Behavior of Bergman metric under quasiconformal deformations" Proc.6th Internat.Colloq.Finite or Infinite Complex Analysis,Andon 1998.
[Publications] M.Yoshida: "On some bilinear forms" Proc.Sixth Internat.Colloq.Finite or Infinite Dimensional Complex Analysis,Andong. 184-187 (1998)
[Publications] S.Saitoh 他3名(Eds.): "Reproducing Kernels and Their Applications" Kluwer Academic Publishers,Boston/Dordrecht/London (to be publishied),

1998 Fiscal Year Annual Research Report

幾何学的複素解析

Principal Investigator

野口 潤次郎 東京大学, 大学院・数理科学研究科, 教授 (20033920)

Research Products

[Publications] Y.Aihara: "Finiteness theorems for meromorphic mappings" Osaka J.Math.35. 593-618 (1998)

[Publications] H.Fujimoto: "Uniqueness problem with truncated multiplicities in value distribution theory" Nagoya Math.J.152. 1-21 (1998)

[Publications] H.Fujimoto: "Uniqueness problem with truncated multiplicities in value distribution theory II" to appear in Nagoya Math.J.

[Publications] Y.Itokawa and R.Kobayashi: "Minimizing currents in open manifolds and the n-1 homology of nonnegatively Ricci curved manifolds" to appear in Amer.J.Math.

[Publications] T.Jimbo and A.Sakai: "Polynomially convex hulls of graphs on the sphere" to appear in Proc.Amer.Math.Soc.

[Publications] J.Kamimoto: "Singularities of the Bergman kernel for certain weakly pseudoconvex domains" J.Math.Scie.Univ.Tokyo. 5. 99-117 (1998)

[Publications] J.Kamimoto: "Asympotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in C^2" Ann.Faculte Scie.Toulouse. 6. 51-86 (1998)

[Publications] J.Kamimoto: "On an integral of Hardy and Littlewood" Kyushu J.Math.52. 249-263 (1998)

[Publications] J.Kamimoto: "The Bergman kernel on certain decoupled domains" to appear in Proc.ISAAC Congress Reproducing Kernels and Their Applications,Kluwer Acad.Publ.

[Publications] J.Kamimoto: "On the multiplicities of the zeros of Laguerre-Polya functions" to appear in Proc.Amer.Math.Sco.

[Publications] J.Kamimoto: "On the singularities of non-analytic Szego kernels" to appear in J.Math.Scie.Univ.Tokyo.

[Publications] J.Kamimoto: "Remarks on Bloch functions on weakly pseudoconvex domains" 京都大学数理解析研究所講究録「再生核の理論とその応用」. 1067. 83-88 (1998)

[Publications] J.Kamimoto: "On an approximation on L^1(R^n)" 京都大学数理解析研究所講究録. (掲載予定).

[Publications] M.Kato: "Schwarz maps of _3F_2 with finite irreducible monodromy groups" Kyushu J.Math.52. 475-495 (1998)

[Publications] S.Mori: "Elimination of defects of meromorphic mappings of C^m into P^n(C)" to appear in Annal.Acad.Scie.Fennicae.Math.23. (1998)

[Publications] N.Niwa,T.Jimbo and S.Owa: "Hardy class of functions defined by the Salagean operator" Annal.Polonici Math.69. 25-30 (1998)

[Publications] J.Noguchi: "On holomorphic curves in semi-Abelian varieties" Math.Z.228. 713-721 (1998)

[Publications] J.Noguchi: "Value distribution theory of holomorphic mappings" Contemp.Math.Amer.Math.Soc.222. 109-129 (1999)

[Publications] T.Okuma: "The second pluri-genus of surface singularities" Compo.Math.110. 263-276 (1998)

[Publications] T.Okuma: "The pluri-genera of surface singularities" Tohoku Math.J.50. 119-132 (1998)

[Publications] T.Okuma: "The plurigenera of Gorenstein surface singularities" Manuscripta Math.94. 187-194 (1997)

[Publications] S.Saitoh and M.Yamamoto: "Intergral transforms involving smooth functions" to appear in Reproducing Kernels and Their Applications,Kluwer Academic Publishers,Boston.

[Publications] S.Saitoh: "Applications of the general theory of reproducing kernels" to appear in Reproducing Kernels and Their Applications,Kluwer Academic Publishers,Boston.

[Publications] S.Saitoh: "Nonlinear transforms and analyticity of functions" to appear in Nonlinear Mathematical Analysis and its Applications Halronic Press.Inc.,Florida,USA.

[Publications] S.Takayama: "Adjoint linear series on weakly 1-complete Kahler manifolds I: Global projective embedding" Math.Ann.311. 501-531 (1998)

[Publications] S.Takayama: "Adjoint linear series on weakly 1-complete kahler manifolds II: Lefschetz type theorem on quasi-Abelian varieties" Math.Ann.312. 363-385 (1998)

[Publications] H.Yamaguchi and F.Maitani: "Behavior of Bergman metric under quasiconformal deformations" Proc.6th Internat.Colloq.Finite or Infinite Complex Analysis,Andon 1998.

[Publications] M.Yoshida: "On some bilinear forms" Proc.Sixth Internat.Colloq.Finite or Infinite Dimensional Complex Analysis,Andong. 184-187 (1998)

[Publications] S.Saitoh 他3名(Eds.): "Reproducing Kernels and Their Applications" Kluwer Academic Publishers,Boston/Dordrecht/London (to be publishied),

野口潤次郎東京大学, 大学院・数理科学研究科, 教授 (20033920)