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29 March 2024
 
  » arxiv » arxiv.0705.3252

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The Hilbert 3/2 Structure and Weil-Petersson Metric on the Space of the Diffeomorphisms of the Circle Modulo Conformal Maps
M. Schonbek ; A. Todorov ; J. Zubelli ;
Date 22 May 2007
Subject Mathematical Physics (math-ph)
AbstractWe gave a new very simple proof that the completion of the space of the diffeomorphism of the circle modulo conformal maps with respect to the Weil-Petersson Metric is a complex analytic manifold modeled on the Hilbert space with 3/2 Sobolev norm. Our proof is based on the analogue of the Hadamard Theorem that the exponentila map is a complex analytic map from the tanegnt space of a point of a simply connected manifold to the manifold.
Source arXiv, arxiv.0705.3252
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