An isometry theorem for quadratic differentials on Riemann surfaces of finite genus
Author:
Nikola Lakic
Journal:
Trans. Amer. Math. Soc. 349 (1997), 29512967
MSC (1991):
Primary 32G15; Secondary 30C62, 30C75
MathSciNet review:
1390043
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Abstract: Assume both and are Riemann surfaces which are subsets of compact Riemann surfaces and respectively, and that the set has infinitely many points. We show that the only surjective complex linear isometries between the spaces of integrable holomorphic quadratic differentials on and are the ones induced by conformal homeomorphisms and complex constants of modulus 1. It follows that every biholomorphic map from the Teichmüller space of onto the Teichmüller space of is induced by some quasiconformal map of onto . Consequently we can find an uncountable set of Riemann surfaces whose Teichmüller spaces are not biholomorphically equivalent.
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Additional Information
Nikola Lakic
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14853
Email:
Nikola@math.cornell.edu
DOI:
http://dx.doi.org/10.1090/S0002994797017716
PII:
S 00029947(97)017716
Received by editor(s):
December 1, 1994
Received by editor(s) in revised form:
February 26, 1996
Article copyright:
© Copyright 1997
American Mathematical Society
