Local and Global Aspects of Weil-Petersson Geometry

Sumio Yamada

Local and Global Aspects of Weil-Petersson Geometry

Differential Geometry 2014-02-19 v2 Mathematical Physics Complex Variables Metric Geometry math.MP

Authors: Sumio Yamada

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.

Keywords

weil-petersson geometry teichmuller spaces differential geometry negative sectional curvature convexity cat(0) geometry coxeter theory riemannian geometry

Cite

@article{arxiv.1206.2083,
  title  = {Local and Global Aspects of Weil-Petersson Geometry},
  author = {Sumio Yamada},
  journal= {arXiv preprint arXiv:1206.2083},
  year   = {2014}
}

Comments

To appear as a chapter in Handbook of Teichmuller Theory, Volume IV

Local and Global Aspects of Weil-Petersson Geometry

Abstract

Keywords

Cite

Comments

Related papers