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Infinitesimal Liouville Distributions for Teichmüller space
Author(s) -
Šarić Dragomir
Publication year - 2004
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611503014539
Subject(s) - mathematics , infinitesimal , space (punctuation) , pure mathematics , mathematical analysis , computer science , operating system
We consider an arbitrary Riemann surface X , possibly of infinite hyperbolic area. The Liouville measure of the hyperbolic metric defines a measure on the space G ( X ~ ) of geodesics of the universal coveringX ~of X . As we vary the Riemann surface structure, this gives an embedding from the Teichmuller space of X into the Fréchet space of Hölder distributions on G ( X ~ ) . We show that the embedding is continuously differentiable. In particular, we obtain an explicit integral representation of the tangent map. 2000 Mathematics Subject Classification 30F60, 32G15 (primary), 46F99 (secondary).