Local and Global Aspects of Weil-Petersson Geometry

Sumio Yamada

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arXiv · 1206.2083

Local and Global Aspects of Weil-Petersson Geometry

Sumio Yamada

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Abstract

This is a survey paper on the topic of Weil-Petersson geometry of Teichmuller spaces. Even though historically the subject has been developed as a branch of complex analysis, the treatment here is from the view-point of differential geometry, much influenced by the works of Eells, Earle, Fischer, Tromba and Wolpert over the several decades. The Weil-Petersson geometry has negative sectional curvature, and the main theme of this article is to exploit the convexity of the Weil-Petersson distance function induced by the negativity of the curvature, from Riemannian geometric approaches as well as those of the CAT(0) geometry and Coxeter theory.

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BibTeX RIS

Sumio Yamada. 2014-02-18. Local and Global Aspects of Weil-Petersson Geometry. https://arxiv.org/abs/1206.2083

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