Liouville and Carath\'eodory coverings in Riemannian and complex geometry

Vladimir Lin; Mikhail Zaidenberg

Liouville and Carath\'eodory coverings in Riemannian and complex geometry

alg-geom 2008-02-03 v2 Algebraic Geometry

Authors: Vladimir Lin , Mikhail Zaidenberg

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 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?

Keywords

Liouville manifold Carathéodory hyperbolic Galois covering harmonic function holomorphic function

Cite

@article{arxiv.alg-geom/9611020,
  title  = {Liouville and Carath\'eodory coverings in Riemannian and complex geometry},
  author = {Vladimir Lin and Mikhail Zaidenberg},
  journal= {arXiv preprint arXiv:alg-geom/9611020},
  year   = {2008}
}

Comments

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

Liouville and Carath\'eodory coverings in Riemannian and complex geometry

Abstract

Keywords

Cite

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