Research on rigidity and finiteness for holomorphic mappings on complex hyperbolic manifolds

复双曲流形上全纯映射的刚性和有限性研究

• 批准号: 13640156
• 负责人: SHIGA Hiroshige
• 金额: $ 2.56万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640156/
• 关键词: Hyperbolic Manifold; Fuchsian group; Complex dynamics; ファック群

We consider holomorphic mappings from an m-dimensional complex hyperbolic manifold M to an n-dimensional complex manifold N represented by a quotient space of a bounded domain N' of the complex space via a discrete automorphism group of N'. We show that if M is of divergence type, then the dimension of the space of the holomorphic mappings from M to N is bounded by the essential boundary dimension of N'. In particular, we may show a finiteness theorem for dominant holomorphic mappings from M to N. We also consider holomorphic mappings on compact Riemann surfaces and their dynamics.

我们考虑了一个M维复双曲流形M到一个N维复流形N的全纯映射，该N维复流形由复空间的有界域N‘的商空间表示，通过一个离散自同构群N’。我们证明了如果M是散度型，则从M到N的全纯映射空间的维数由N'的本质边界维数所限定。特别地，我们可以证明从M到n的全纯映射的有限性定理。我们还考虑紧致黎曼曲面上的全纯映射及其动力学。

项目成果

H.Sumi: "Skew product maps related to finitely generated rational semigroups"Nonlinearity. 13. 995-1019 (2000)

H.Sumi：“与有限生成的有理半群相关的偏斜积图”非线性。

H.Shiga: "Dirichlet solutions on bordered Riemann surfaces and quasiconformal mappings"J. d'Analyse. Math.. to appear.

H.Shiga：“有界黎曼曲面上的狄利克雷解和拟共形映射”J。

H.Kriete, H.Sumi: "Semihyperbolic transcendental semigroups"J.Math.Kyoto Univ.. 40-2. 205-216 (2000)

H.Kriete，H.Sumi：“半双曲超越半群”J.Math.Kyoto Univ.. 40-2。

Shiga, H.: "On holomorphic mappings of complex manifolds with model."J.Math.Soc.Japan.. (to appear).

Shiga, H.：“关于带有模型的复流形的全纯映射。”J.Math.Soc.Japan..（待发表）。

M.Tanbe: "Bounds on the number of holomorphic maps of compact Riemann surfaces,"Proc.Amer.Math.Soc.. (To appear).

M.Tanbe：“紧致黎曼曲面全纯映射数量的界限”，Proc.Amer.Math.Soc..（即将出现）。