Geometric Isomorphisms between Infinite Dimensional Teichmüller Spaces

  title={Geometric Isomorphisms between Infinite Dimensional Teichmüller Spaces},
  author={Frederick P. Gardiner},
Let X and Y be the interiors of bordered Riemann surfaces with finitely generated fundamental groups and nonempty borders. We prove that every holomorphic isomorphism of the Teichmüller space of X onto the Teichmüller space of Y is induced by a quasiconformal homeomorphism of X onto Y . These Teichmüller spaces are not finite dimensional and their groups of holomorphic automorphisms do not act properly discontinuously, so the proof presents difficulties not present in the classical case. To… CONTINUE READING
Highly Cited
This paper has 17 citations. REVIEW CITATIONS


Publications referenced by this paper.
Showing 1-10 of 14 references


H. M. Farkas, I. Kra, +3 authors New York
Berlin, • 1992

The Schwarz Lemma

S. Dineen
Oxford, • 1989

John Wiley and Sons

S. Nag, The Complex Analytic Theory of Teichmüller Spaces
New York, • 1988

Advances in Holomorphy (J

L. A. Harris, Schwarz-Pick systems of pseudometrics for domains in normed lin spaces
A. Barroso, ed.), North-Holland Mathematics Series 34, North-Holland, Amsterdam, New York, Oxford, • 1979

A foliation of Teichmüller space by twist invariant

A. Marden, H. Masur
disks, Math. Scand • 1975

On quadratic differentials and extremal quasiconformal mappings

K. Strebel
Proceedings Int. Congr. Math. Vancouver 1974, • 1975

On holomorphic mappings between Teichmüller spaces, Contributions to Analysis (L

C. J. Earle, I. Kra
V. Ahlfors et al., eds.), • 1974


I. Kra, Automorphic Forms, Kleinian Groups, Benjamin
Massachusetts, • 1972

Automorphisms and isometries of Teichmüller space, Advances in the Theory of Riemann Surfaces (L

H. Royden
V. Ahlfors et al., eds.), Ann. Math. Stud • 1971

On a theorem of Dixmier

K.-F. Ng
Math. Scand • 1971

Similar Papers

Loading similar papers…