1999 Fiscal Year Final Research Report Summary
Complex analysis of Bergman spaces and α-cohomology
| Project/Area Number |
10440041
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Nagoya University |
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Principal Investigator |
OHSAWA Takeo Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (30115802)
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| Co-Investigator(Kenkyū-buntansha) |
KITAOKA Yoshiyuki Nagoya Univ., Professor, 大学院・多元数理科学研究科, 教授 (40022686)
SUZUKI Noriaki Nagoya Univ., Associate Professor, 大学院・多元数理科学研究科, 助教授 (50154563)
NAKANISHI Toshihiro Nagoya Univ., Associate Professor, 大学院・多元数理科学研究科, 助教授 (00172354)
YAMATO kazuo Nagoya Univ., Associate Professor, 大学院・多元数理科学研究科, 助教授 (30022677)
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| Project Period (FY) |
1998 – 1999
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| Keywords | Bergman Kernel / LィイD12ィエD1 holomorphic function / Pseudoconvex domain / Bergman metric / Complexification of gid / Extension theorem / Division theorem |
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| Research Abstract |
Bergman metric of bounded balanced pseudoconvex domains in CィイD1nィエD1 was studied. A quantitative result implying the completeness first due to Jarnicki-Pflug was obtained. Singular fiber metric was used to obtain as estimate for the Bergman kernel function on pseudoconvex domains in PィイD1nィエD1. A new phenomenon encountere was that locally hyperconvex domains in PィイD1nィエD1 are not necessarily globally hyperconvex. As for the domains with smooth boundary existence of bounded p.s.h. functions was proved. In case the boundary is real analytic, it was proved that such a pseudoconvex domain must be strictly pseudoconvex at some boundary point. More recently, a generalization of an LィイD12ィエD1 extension theorem to complex manifolds was obtained, which has, as a corollary, a famous LィイD12ィエD1 division theorem of Skoda.
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