Weighted Ricci curvature estimates for Hilbert and Funk geometries

Details Weighted Ricci curvature estimates for Hilbert and Funk geometries Weighted Ricci curvature estimates for Hilbert and Funk geometries

2012-03-09

arxiv.org/abs/1203.2001v1

Mathematics

Differential Geometry

12 pages

Scientific paper

We consider Hilbert and Funk geometries on a strongly convex domain in the Euclidean space. We show that, with respect to the Lebesgue measure on the domain, Hilbert (resp. Funk) metric has the bounded (resp. constant negative) weighted Ricci curvature. As one of corollaries, these metric measure spaces satisfy the curvature-dimension condition in the sense of Lott, Sturm and Villani.

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