Bounded holomorphic functions on negatively curved Kähler manifolds of dimension $\ge 3$

Jianguo Cao; Mei-Chi Shaw

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arXiv · 1512.00368

Bounded holomorphic functions on negatively curved Kähler manifolds of dimension $\ge 3$

Jianguo Cao·Mei-Chi Shaw

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Abstract

Let M be a simply-connected complete Kahler manifold whose sectional curvature is bounded between two negative numbers. In this paper we prove the existence of non-constant bounded holomorphic functions on M if the complex dimension of M is greater or equal to three. Our proof uses bounded plurisubharmonic exhaustion functions, the Cauchy-Riemann equations and uniform Holder estimates for CR functions on geodesic spheres.

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BibTeX RIS

Jianguo Cao, Mei-Chi Shaw. 2016-02-06. Bounded holomorphic functions on negatively curved Kähler manifolds of dimension $\ge 3$. https://arxiv.org/abs/1512.00368

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