On Picard's Problem via Nevanlinna Theory
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915874702622720 |
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| author | Dong, Xianjing |
| author_facet | Dong, Xianjing |
| contents | We consider the classical Picard's problem for non-parabolic complete Kähler manifolds with non-negative Ricci curvature. Based on the global Green function approach, we give a positive answer to Picard's problem under certain condition by developing Nevanlinna theory. That is, we prove that every meromorphic function on such a manifold reduces to a constant if it omits three distinct values, provided that the manifold satisfies a volume growth condition; and prove that every meromorphic function of non-polynomial type growth on such a manifold can avoid 2 distinct values at most. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09659 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Picard's Problem via Nevanlinna Theory Dong, Xianjing Complex Variables 32H30, 32H25 We consider the classical Picard's problem for non-parabolic complete Kähler manifolds with non-negative Ricci curvature. Based on the global Green function approach, we give a positive answer to Picard's problem under certain condition by developing Nevanlinna theory. That is, we prove that every meromorphic function on such a manifold reduces to a constant if it omits three distinct values, provided that the manifold satisfies a volume growth condition; and prove that every meromorphic function of non-polynomial type growth on such a manifold can avoid 2 distinct values at most. |
| title | On Picard's Problem via Nevanlinna Theory |
| topic | Complex Variables 32H30, 32H25 |
| url | https://arxiv.org/abs/2405.09659 |