The Journal of Geometric Analysis

, Volume 28, Issue 4, pp 3690–3707 | Cite as

Closed Groups of Automorphisms of Products of Hyperbolic Riemann Surfaces

  • Evgeny A. PoletskyEmail author
  • Sergey E. Sharonov


In this paper, we provide the complete list of all closed groups G of automorphisms of a product R of hyperbolic Riemann surfaces such that the order of any element in \(\textit{G/G}_e\), where \(G_e\) is the identity component of G, is finite. In particular, if X is an analytic subvariety of R then the identity component of the stabilizer of X in \({\text {Aut}}R\) is on this list. In its turn, it allows us to state that the identity component of the group \({\text {Aut}}X\) must contain a group from this list.


Automorphisms of complex manifolds Stabilizers Exponential Lie groups Non-discrete subgroups 

Mathematics Subject Classification

Primary 32M05 Secondary 54H15 



We would like to thank G. Prasad for his suggestion for the proof of Theorem 4.8. We are also grateful to the referee whose corrections and comments significantly improved the exposition.


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© Mathematica Josephina, Inc. 2017

Authors and Affiliations

  1. 1.Department of MathematicsSyracuse UniversitySyracuseUSA

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