Weighted Ricci curvature estimates for Hilbert and Funk geometries (Q374435)

The Hilbert and Funk metrics are important examples of Finsler metrics and have many important applications in other fields. In this paper, the author considers the weighted Ricci curvature of these metrics. Weighted Ricci curvature was introduced by the author in a previous paper [Calc. Var. Partial Differ. Equ. 36, No. 2, 211--249 (2009; Zbl 1175.49044)], and has interesting applications in analysis and geometry. It is shown that the Hilbert and Funk metrics have respectively bounded and constant negative weighted Ricci curvature, with respect to the Lesbegue measure on the domain where the metric is defined.