Israel Journal of Mathematics

, Volume 12, Issue 4, pp 400–407 | Cite as

A remark on Mumford’s compactness theorem

  • Lipman Bers


It is shown that a recent compactness theorem for Fuchsian groups, due to Mumford, remains valid for groups containing elliptic and parabolic elements.


Conjugacy Class Quasiconformal Mapping Compactness Theorem Fuchsian Group Compact Riemann Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. Bers,Uniformization by Beltrami equations, Comm. Pure Appl. Math.14 (1961), 215–228.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    L. Bers,Uniformization, moduli and Kleinian groups, Bull. London Math. Soc., to appear.Google Scholar
  3. 3.
    R.H. Fox,On Fenchel’s conjecture about F-Groups, Mat. Tidsskr. B (1952), 61–65.Google Scholar
  4. 4.
    R. Fricke and F. Klein,Vorlseungen über die Theorie der automorphen Funktionen, Vol. 1, Teubner, 1897.Google Scholar
  5. 5.
    D. Mumford,A remark on Mahler’s compactness theorem, Proc. Amer. Math. Soc.28 (1917), 289–294.CrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1972

Authors and Affiliations

  • Lipman Bers
    • 1
    • 2
    • 3
  1. 1.Columbia UniversityNew York
  2. 2.Technion-Israel Institute for TechnologyHaifa
  3. 3.The Weizmann InstituteRehovot

Personalised recommendations