2017 Fiscal Year Final Research Report
Higher order pseudoconvexity for domains with Levi-flat boundary
Project/Area Number |
26800057
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Basic analysis
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Research Institution | Shizuoka University (2017) Tokyo University of Science (2015-2016) Nagoya University (2014) |
Principal Investigator |
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Research Collaborator |
Brinkschulte Judith Universität Leipzig, Mathematisches Institut, Wissenschaftlicher Mitarbeiter
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Project Period (FY) |
2014-04-01 – 2018-03-31
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Keywords | レビ平坦曲面 / 複素解析幾何 / 多変数関数論 / 葉層構造論 / 微分幾何学 / ポテンシャル論 / エルゴード理論 / 国際情報交換 |
Outline of Final Research Achievements |
This research project focused on Levi-flats, manifolds foliated by complex manifolds. Combining ideas from complex analysis, theory of dynamical system, and differential geometry, we obtained following results: We improved known curvature restrictions for hypothetical Levi-flats in complex projective planes. We proved an inequality for the Diederich-Fornaess index on abstract Levi-flats. We gave potential theoretic proof for non-existence of bounded holomorphic functions on bi-disk invariant by the diagonal action of Fuchsian groups without relying on ergodicity theorems, and also found an explicit construction for such invariant holomorphic functions by means of integral transformations.
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Free Research Field |
複素解析幾何学
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