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arXiv · 0705.3252

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
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Abstract

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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M. Schonbek, A. Todorov, J. Zubelli. 2007-05-24. The Hilbert 3/2 Structure and Weil-Petersson Metric on the Space of the Diffeomorphisms of the Circle Modulo Conformal Maps. https://arxiv.org/abs/0705.3252

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