Bounded domains on Kobayashi hyperbolic manifolds covering compact complex manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912803366895616 |
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| author | Newsome, Nicholas |
| author_facet | Newsome, Nicholas |
| contents | The lack of a uniformization theorem in several complex variables leads to a desire to classify all of the simply connected domains. We use established computational methods and a localization technique to generalize a recently-published classification. In particular, we show that if a domain with $C^{1,1}$ boundary on a Kobayashi hyperbolic complex manifold contains a totally real boundary point and covers a compact manifold, then its universal cover must be the Euclidean ball. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03935 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounded domains on Kobayashi hyperbolic manifolds covering compact complex manifolds Newsome, Nicholas Complex Variables The lack of a uniformization theorem in several complex variables leads to a desire to classify all of the simply connected domains. We use established computational methods and a localization technique to generalize a recently-published classification. In particular, we show that if a domain with $C^{1,1}$ boundary on a Kobayashi hyperbolic complex manifold contains a totally real boundary point and covers a compact manifold, then its universal cover must be the Euclidean ball. |
| title | Bounded domains on Kobayashi hyperbolic manifolds covering compact complex manifolds |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2504.03935 |