The Hilbert 3/2 Structure and Weil-Petersson Metric on the Space of the Diffeomorphisms of the Circle Modulo Conformal Maps

Details The Hilbert 3/2 Structure and Weil-Petersson Metric on the Space of the Diffeomorphisms of the Circle Modulo Conformal Maps The Hilbert 3/2 Structure and Weil-Petersson Metric on the Space of the Diffeomorphisms of the Circle Modulo Conformal Maps

2007-05-22

arxiv.org/abs/0705.3252v2

Physics

Mathematical Physics

A refernce to a Corollary was corrected

Scientific paper

We 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.

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