Closed Groups of Automorphisms of Products of Hyperbolic Riemann Surfaces

Evgeny Alexander Poletsky, Sergey E. Sharonov

Research output: Contribution to journalArticle


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 (Formula presented.), where (Formula presented.) 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 (Formula presented.) is on this list. In its turn, it allows us to state that the identity component of the group (Formula presented.) must contain a group from this list.

Original languageEnglish (US)
Pages (from-to)1-18
Number of pages18
JournalJournal of Geometric Analysis
StateAccepted/In press - Dec 11 2017



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

ASJC Scopus subject areas

  • Geometry and Topology

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