Liouville and Carathéodory coverings in Riemannian and complex geometry
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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?
20 pages, AMSTeX. A revised version. The proof of Theorem 3.1 has been completed, and some other minor correction has been done
20 pages, AMSTeX. A revised version. The proof of Theorem 3.1 has been completed, and some other minor correction has been done