Infinitesimal Liouville Distributions for Teichmüller Space

• Autores: Dragomir Saric
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 88, Nº 2, 2004, págs. 436-454
• Idioma: inglés
• DOI: 10.1112/s0024611503014539
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• Resumen

  • 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 $G(\tilde{X})$ of geodesics of the universal covering $\tilde{X}$ of $X$. As we vary the Riemann surface structure, this gives an embedding from the Teichmüller space of $X$ into the Fréchet space of Hölder distributions on $G(\tilde{X})$. We show that the embedding is continuously differentiable. In particular, we obtain an explicit integral representation of the tangent map.