An isometry theorem for quadratic differentials on Riemann surfaces of finite genus

被引:24
|
作者
Lakic, N
机构
关键词
D O I
10.1090/S0002-9947-97-01771-6
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Assume both X and Y are Riemann surfaces which are subsets of compact Riemann surfaces X-1 and Y-1, respectively, and that the set X-1 - X has infinitely many points. We show that the only surjective complex linear isometries between the spaces of integrable holomorphic quadratic differentials on X and Y are the ones induced by conformal homeomorphisms and complex constants of modulus 1. It follows that every biholomorphic map from the Teichmuller space of X onto the Teichmuller space of Y is induced by some quasiconformal map of X onto Y. Consequently we can find an uncountable set of Riemann surfaces whose Teichmuller spaces are not biholomorphically equivalent.
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页码:2951 / 2967
页数:17
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