Convex bodies in Euclidean and Weil-Petersson geometries
arXiv:1110.5022
Abstract
On a convex body in a Euclidean space, we introduce a new variational formulation for its Funk metric, a Finsler metric compatible with the tautological Finsler structure of the convex body. We generalize the metric on Teichmuller spaces with the Weil-Petersson distance function. A set of similarities the resulting metric structure shares with Thurston's asymmetric metric is noted.
15 pages, to be published in Proceedings of the AMS, Version 2 contains modifications in 3.4