Research on analytic mappings on manifolds
| Project/Area Number |
61302006
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| Research Category |
Grant-in-Aid for Co-operative Research (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
SUITA Nobuyuki Faculty of Science, Tokyo Institute of Technology, Professor, 理学部, 教授 (90016022)
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| Co-Investigator(Kenkyū-buntansha) |
NOGUCHI Junjiro Faculty of Science, Tokyo Institute of Technology, Associate Professor, 理学部, 助教授 (20033920)
SAKAI Makoto Faculty of Science, Tokyo Metropolitan University, Professor, 理学部, 教授 (70016129)
TODA Nobushige Faculty of Engineering, Nagoya Institute of Technology, Professor, 工学部, 教授 (30004295)
SATO Hiroki Faculty of Science, Shizuoka University, Professor, 理学部, 教授 (40022222)
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| Project Period (FY) |
1986 – 1987
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| Project Status |
Completed (Fiscal Year 1987)
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| Budget Amount *help |
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 1987: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 1986: ¥3,000,000 (Direct Cost: ¥3,000,000)
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| Keywords | Self-Conformal Mapping / Analytic Map / H_P Space / Removable Singularity / Bounded Analytic Functions / Analytic Capacity / Value Distribution Theory / 多変数函数論 / ハーディ空間 / ブロック・ランダウ定数 / タイヒミュラー空間 / フックス群 / 等角計量 / 正則〓 / ポランシアル論 / 多変数解析函数 |
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| Research Abstract |
First of all, the group of self-conformal mappings of closed Riemann surfaces of genus five is completely characterized (Kuribayashi-Kimura). We obtained a good bound of the number of boundary preserving analytic mappings of an n-ply plane region, (n-1)2^<4n-6>,which is better than a bound due to a result of Howard and Sommes (Jenkins-Suita). A problem remained is to extend this result for compact Riemann surfaces of genus greater than two. Kobayashi and Suita proved an H^p norm identity for analytic mappings of finite area on a hyperbolic Riemann surfaces. This result is extwnded to an estimate of the best harmonic majorant of the norm function IIxII^p on a domain of finite volume in R^n. This result has an application to the Brownian motion. As to bounded analytic functions Hayashi studied the structure of maximal ideal spaces. Separation properties by bounded analytic function for a covering surface is investigated by Hayashi and Nakai. Murai studied some properties of analytic capasity. Suxuki proved removability of a compact set E of capasity zero for analytic mappings from the unit disc less E into a compact Riemann surface of genus 2.This result has a generalization for higher dimensional cases. Noguchi studied hyperbolic geometry, using the value distribution theory, and generalized the big Picard theorem. He applied his results to the moduli problem and the diophantine geomwtry. A nice result for the munber of exceptional direction of the Gauss map of a complete minimal surface is obtained by Fujimoto. Toda studied meromorphic solutions of algebraic differentialequation through the value distribution theory.
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Report
(2 results)
Research Products
(16 results)
