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Coherence of Limit Points in the Fibers over the Asymptotic Teichmüller Space

Coherence of Limit Points in the Fibers over the Asymptotic Teichmüller Space We consider the infinite dimensional Teichmüller space of a Riemann surface of general type. On the basis of the fact that the action of the quasiconformal mapping class group on the Teichmüller space is not discontinuous, in general, we divide the Teichmüller space into two disjoint subsets, the limit set and the region of discontinuity, according to the discreteness of the orbit by a subgroup of the quasiconformal mapping class group. The asymptotic Teichmüller space is a certain quotient space of the Teichmüller space and there is a natural projection from the Teichmüller space to the asymptotic Teichmüller space. We consider the fibers of the projection over any point in the asymptotic Teichmüller space, and show a coherence of the discreteness on each fiber in the Teichmüller space. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Coherence of Limit Points in the Fibers over the Asymptotic Teichmüller Space

Fujikawa, Ege
Computational Methods and Function Theory , Volume 14 (3) – Apr 29, 2014
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Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-014-0066-y
Publisher site
See Article on Publisher Site

Abstract

We consider the infinite dimensional Teichmüller space of a Riemann surface of general type. On the basis of the fact that the action of the quasiconformal mapping class group on the Teichmüller space is not discontinuous, in general, we divide the Teichmüller space into two disjoint subsets, the limit set and the region of discontinuity, according to the discreteness of the orbit by a subgroup of the quasiconformal mapping class group. The asymptotic Teichmüller space is a certain quotient space of the Teichmüller space and there is a natural projection from the Teichmüller space to the asymptotic Teichmüller space. We consider the fibers of the projection over any point in the asymptotic Teichmüller space, and show a coherence of the discreteness on each fiber in the Teichmüller space.

Journal

Computational Methods and Function Theory – Springer Journals

Published: Apr 29, 2014

References

  • Conformally natural extension of homeomorphisms of the circle
    Douady, A; Earle, CJ
  • Geometric isomorphisms between infinite dimensional Teichmüller spaces
    Earle, CJ; Gardiner, FP
  • Asymptotic Teichmüller space. Part I: the complex structure
    Earle, CJ; Gardiner, FP; Lakic, N
  • Asymptotic Teichmüller space. Part II: the metric structure
    Earle, CJ; Gardiner, FP; Lakic, N
  • Barycentric extension and the Bers embedding for asymptotic Teichmüller space
    Earle, CJ; Markovic, V; Saric, D
  • Effectiveness of Teichmüller modular groups. In the tradition of Ahlfors and Bers
    Epstein, AL
  • Limit sets and regions of discontinuity of Teichmüller modular groups
    Fujikawa, E
  • Modular groups acting on infinite dimensional Teichmüller spaces
    Fujikawa, E
  • The action of geometric automorphisms of asymptotic Teichmüller spaces
    Fujikawa, E
  • Pure mapping class group acting on Teichmüller space
    Fujikawa, E
  • Recurrent and periodic points for isometries of $$L^\infty $$ L ∞ spaces
    Fujikawa, E; Matsuzaki, K
  • Non-stationary and discontinuous quasiconformal mapping class groups
    Fujikawa, E; Matsuzaki, K
  • Stable quasiconformal mapping class groups and asymptotic Teichmüller spaces
    Fujikawa, E; Matsuzaki, K
  • On the action of the mapping class group for Riemann surfaces of infinite type
    Fujikawa, E; Shiga, H; Taniguchi, M
  • Teichmüller Theory and Quadratic Differentials
    Gardiner, FP
  • Symmetric structure on a closed curve
    Gardiner, FP; Sullivan, DP
  • Quasiconformal Mappings in the Plane
    Lehto, O; Virtanen, K
  • Biholomorphic maps between Teichmüller spaces
    Markovic, V
  • Inclusion relations between the Bers embeddings of Teichmüller spaces
    Matsuzaki, K
  • A countable Teichmüller modular group
    Matsuzaki, K
  • Quasiconformal mapping class groups having common fixed points on the asymptotic Teichmüller spaces
    Matsuzaki, K
  • Automorphisms and isometries of Teichmüller spaces
    Royden, HL