Nevanlinna Theory on Geodesic Balls of Complete Kähler Manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914918484148224 |
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| author | Dong, Xianjing |
| author_facet | Dong, Xianjing |
| contents | We study Nevanlinna theory of meromorphic mappings from a geodesic ball of a general complete Kähler manifold with non-negative Ricci curvature into a complex projective manifold by introducing a heat kernel method. When dimension of a target manifold is not greater than one of a source manifold, we establish a second main theorem which is a generalization of the classical second main theorem for a ball of $\mathbb C^m.$ If a source manifold is non-compact and it carries a positive global Green function, then we establish a global second main theorem for the source manifold. As a result, we obtain a Picard's theorem for complete Kähler manifolds with non-negative Ricci curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11623 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nevanlinna Theory on Geodesic Balls of Complete Kähler Manifolds Dong, Xianjing Complex Variables 32H30, 32H25 We study Nevanlinna theory of meromorphic mappings from a geodesic ball of a general complete Kähler manifold with non-negative Ricci curvature into a complex projective manifold by introducing a heat kernel method. When dimension of a target manifold is not greater than one of a source manifold, we establish a second main theorem which is a generalization of the classical second main theorem for a ball of $\mathbb C^m.$ If a source manifold is non-compact and it carries a positive global Green function, then we establish a global second main theorem for the source manifold. As a result, we obtain a Picard's theorem for complete Kähler manifolds with non-negative Ricci curvature. |
| title | Nevanlinna Theory on Geodesic Balls of Complete Kähler Manifolds |
| topic | Complex Variables 32H30, 32H25 |
| url | https://arxiv.org/abs/2406.11623 |