On holomorphic functions on negatively curved manifolds

Marijan Markovic

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arXiv · 2109.10264

On holomorphic functions on negatively curved manifolds

Marijan Markovic

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Abstract

Based on a well known Sh.-T. Yau theorem we obtain that the real part of a holomorphic function on a K\"{a}hler manifold with the Ricci curvature bounded from below by $-1$ is contractive with respect to the distance on the manifold and the hyperbolic distance on $(-1,1)$ inhered from the domain $(-1,1)\times\mathbb{R}$. Moreover, in the case of bounded holomorphic functions we prove that the modulus is contractive with respect to the distance on the manifold and the hyperbolic distance on the unit disk.

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Marijan Markovic. 2021-09-21. On holomorphic functions on negatively curved manifolds. https://arxiv.org/abs/2109.10264

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