Liouville and Carathéodory coverings in Riemannian and complex geometry

Details Liouville and Carathéodory coverings in Riemannian and complex geometry Liouville and Carathéodory coverings in Riemannian and complex geometry

1996-11-18

arxiv.org/abs/alg-geom/9611020v2

Mathematics

Algebraic Geometry

20 pages, AMSTeX. A revised version. The proof of Theorem 3.1 has been completed, and some other minor correction has been don

Scientific paper

A Riemannian manifold resp. a complex space $X$ is called Liouville if it carries no nonconstant bounded harmonic resp. holomorphic functions. It is called Carath\'eodory, or Carath\'eodory 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 Carath\'eodory hyperbolic?

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