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Geometric Isomorphisms between
Infinite Dimensional Teichmüller Spaces


Authors: Clifford J. Earle and Frederick P. Gardiner
Journal: Trans. Amer. Math. Soc. 348 (1996), 1163-1190
MSC (1991): Primary 32G15; Secondary 30C62, 30C75
DOI: https://doi.org/10.1090/S0002-9947-96-01490-0
MathSciNet review: 1322950
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Abstract: 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 overcome them we study weak continuity properties of isometries of the tangent spaces to Teichmüller space and special properties of Teichmüller disks.


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Additional Information

Clifford J. Earle
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
Email: cliff@math.cornell.edu

Frederick P. Gardiner
Affiliation: Department of Mathematics, Brooklyn College, City University of New York, Brooklyn, New York 11210
Email: fpgbc@cunyvm.cuny.edu

DOI: https://doi.org/10.1090/S0002-9947-96-01490-0
Received by editor(s): March 15, 1995
Additional Notes: Research of the first author was partly supported by NSF Grant DMS 9206924 and by a grant from MSRI; of the second, by NSF Grant DMS 9204069.
Article copyright: © Copyright 1996 American Mathematical Society

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