Nevanlinna Theory on Geodesic Balls of Complete K\"ahler Manifolds

Xianjing Dong

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arXiv · 2406.11623

Nevanlinna Theory on Geodesic Balls of Complete K\"ahler Manifolds

Xianjing Dong

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Abstract

We study Nevanlinna theory of meromorphic mappings from a geodesic ball of a general complete K\"ahler 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 K\"ahler manifolds with non-negative Ricci curvature.

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BibTeX RIS

Xianjing Dong. 2024-06-17. Nevanlinna Theory on Geodesic Balls of Complete K\"ahler Manifolds. https://arxiv.org/abs/2406.11623

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