Convex bodies in Euclidean and Weil-Petersson geometries

Yamada, Sumio

doi:10.1090/S0002-9939-2013-11841-1

Convex bodies in Euclidean and Weil-Petersson geometries
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Proc. Amer. Math. Soc. 142 (2014), 603-616 Request permission

Abstract:

A variational formulation of Funk metric defined on a convex set in a Euclidean space is introduced. The new definition provides geometric descriptions of the Finsler metric. Secondly, the variational characterization of the Funk metric is generalized to the Weil-Petersson geometry of Teichmüller spaces. Finally, a comparison between several Funk-type metrics defined on Teichmüller spaces is made.

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