Mathematical Research Letters

Volume 11 (2004)

Number 3

On the Geometry of Weil-Petersson Completion of Teichmüller Spaces

Pages: 327 – 344

DOI: http://dx.doi.org/10.4310/MRL.2004.v11.n3.a5

Author

Sumio Yamada

Abstract

Given a surface of higher genus, we will look at the Weil-Petersson completion of the Teichmüller space of the surface, and will study the geometry induced by the Weil-Petersson distance functional. Although the completion is no longer a Riemannian manifold, it has characteristics similar to those of Cartan-Hadamard manifolds.

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