Bergman representative coordinate, constant holomorphic curvature and a multidimensional generalization of Carathéodory's theorem
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909625229508608 |
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| author | Dong, Robert Xin Wong, Bun |
| author_facet | Dong, Robert Xin Wong, Bun |
| contents | By using the Bergman representative coordinate and Calabi's diastasis, we extend a theorem of Lu to bounded pseudoconvex domains whose Bergman metric is incomplete with constant holomorphic sectional curvature. We characterize such domains that are biholomorphic to a ball possibly less a relatively closed pluripolar set. We also provide a multidimensional generalization of Carathéodory's theorem on the continuous extension of the biholomorphisms up to the closures. In particular, sufficient conditions are given, in terms of the Bergman kernel, for the boundary of a biholomorphic ball to be a topological sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_08741 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bergman representative coordinate, constant holomorphic curvature and a multidimensional generalization of Carathéodory's theorem Dong, Robert Xin Wong, Bun Complex Variables Differential Geometry Primary 32F45, Secondary 32H10, 32T05, 32D20 By using the Bergman representative coordinate and Calabi's diastasis, we extend a theorem of Lu to bounded pseudoconvex domains whose Bergman metric is incomplete with constant holomorphic sectional curvature. We characterize such domains that are biholomorphic to a ball possibly less a relatively closed pluripolar set. We also provide a multidimensional generalization of Carathéodory's theorem on the continuous extension of the biholomorphisms up to the closures. In particular, sufficient conditions are given, in terms of the Bergman kernel, for the boundary of a biholomorphic ball to be a topological sphere. |
| title | Bergman representative coordinate, constant holomorphic curvature and a multidimensional generalization of Carathéodory's theorem |
| topic | Complex Variables Differential Geometry Primary 32F45, Secondary 32H10, 32T05, 32D20 |
| url | https://arxiv.org/abs/2209.08741 |