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arXiv · alg-geom/9611020

Liouville and Carathéodory coverings in Riemannian and complex geometry

Vladimir Lin·Mikhail Zaidenberg
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Abstract

A Riemannian manifold resp. a complex space $X$ is called Liouville if it carries no nonconstant bounded harmonic resp. holomorphic functions. It is called Carathéodory, or Carathéodory hyperbolic, if bounded harmonic resp. holomorphic functions separate the points of $X$. The problems which we discuss in this paper arise from the following question: When a Galois covering $X$ with Galois group $G$ over a Liouville base $Y$ is Liouville or, at least, is not Carathéodory hyperbolic?

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BibTeXRIS

Vladimir Lin, Mikhail Zaidenberg. 1997-04-11. Liouville and Carathéodory coverings in Riemannian and complex geometry. https://arxiv.org/abs/alg-geom/9611020

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