Dynamics on teichmüller spaces and self-covering of riemann surfaces

Ege Fujikawa, Katsuhiko Matsuzaki, Masahiko Taniguchi

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

A non-injective holomorphic self-cover of a Riemann surface induces a non-surjective holomorphic self-embedding of its Teichmüller space. We investigate the dynamics of such self-embeddings by applying our structure theorem of self-covering of Riemann surfaces and examine the distribution of its isometric vectors on the tangent bundle over the Teichmüller space. We also extend our observation to quasiregular self-covers of Riemann surfaces and give an answer to a certain problem on quasiconformal equivalence to a holomorphic self-cover.

Original languageEnglish
Pages (from-to)865-888
Number of pages24
JournalMathematische Zeitschrift
Volume260
Issue number4
DOIs
Publication statusPublished - 2008 Dec
Externally publishedYes

Fingerprint

Riemann Surface
Covering
Cover
Quasiconformal
Tangent Bundle
Structure Theorem
Isometric
Equivalence

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Dynamics on teichmüller spaces and self-covering of riemann surfaces. / Fujikawa, Ege; Matsuzaki, Katsuhiko; Taniguchi, Masahiko.

In: Mathematische Zeitschrift, Vol. 260, No. 4, 12.2008, p. 865-888.

Research output: Contribution to journalArticle

Fujikawa, Ege ; Matsuzaki, Katsuhiko ; Taniguchi, Masahiko. / Dynamics on teichmüller spaces and self-covering of riemann surfaces. In: Mathematische Zeitschrift. 2008 ; Vol. 260, No. 4. pp. 865-888.
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