Discrete groups and holomorphic functions

We determine conditions under which the quotient of a Kähler-Hadamard manifold by a torsion-free, discrete group of isometries admits a big set of nontrivial holomorphic functions. We also generalize a theorem of G. A. Margulis on centerless of cocompact discrete groups of automorphisms of a Carathé...

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Bibliographic Details
Published inMathematische annalen Vol. 355; no. 3; pp. 1025 - 1047
Main Author Chen, Bo-Yong
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.03.2013
Subjects
Mathematics
Mathematics and Statistics
32M15
32Q05
32E10
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Summary:We determine conditions under which the quotient of a Kähler-Hadamard manifold by a torsion-free, discrete group of isometries admits a big set of nontrivial holomorphic functions. We also generalize a theorem of G. A. Margulis on centerless of cocompact discrete groups of automorphisms of a Carathéodory hyperbolic manifold by a different approach based on the Carathéodory pseudodistance.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-012-0810-4