K$\ddot{\operatorname{a}}$hlerity of invariant metrics on pseudoconvex domain of dimension two
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911125759590400 |
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| author | Wang, Lang |
| author_facet | Wang, Lang |
| contents | For a two dimensional bounded pseudoconvex domain of finite type, we prove uniformization theorems via K$\ddot{\operatorname{a}}$hler-Kobayashi metric or K$\ddot{\operatorname{a}}$hler-Carath$\acute{\operatorname{e}}$odory metric with quasi-finite geometry of order three. In particular, a pseudoconvex Reinhardt domain of finite type is the unit ball if and only if the Bergman metric is a scalar multiple of the Kobayashi metric or Carath$\acute{\operatorname{e}}$odory metric. Moreover, we establish a rigidity theorem concerning holomorphic sectional curvature of Bergman metric and Lu constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19992 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | K$\ddot{\operatorname{a}}$hlerity of invariant metrics on pseudoconvex domain of dimension two Wang, Lang Complex Variables For a two dimensional bounded pseudoconvex domain of finite type, we prove uniformization theorems via K$\ddot{\operatorname{a}}$hler-Kobayashi metric or K$\ddot{\operatorname{a}}$hler-Carath$\acute{\operatorname{e}}$odory metric with quasi-finite geometry of order three. In particular, a pseudoconvex Reinhardt domain of finite type is the unit ball if and only if the Bergman metric is a scalar multiple of the Kobayashi metric or Carath$\acute{\operatorname{e}}$odory metric. Moreover, we establish a rigidity theorem concerning holomorphic sectional curvature of Bergman metric and Lu constant. |
| title | K$\ddot{\operatorname{a}}$hlerity of invariant metrics on pseudoconvex domain of dimension two |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2508.19992 |