A universal volume comparison theorem for Finsler manifolds and related results (Q2862947)

The paper is organized in the following way: Section 2 contains preliminaries on Finsler geometry and on the volume form, respectively. The Finsler version of the Calabi-Yau volume and universal volume comparison theorem are presented in Section 3. The generalized Berger-Kazdan inequality is presented in Section 4 and the Section 5 is dedicated to the genera1ized Santaló formula. Based on these, the Croke-type isoperimetric inequality is studied in Section 6. The relations between the volume forms on Finsler manifolds are given.NEWLINENEWLINE Reviewer's remark: Having this structure \(g\), the total space of the tangent bundle can be endowed with a non-linear connection \(N\). There exists a \(N\)-linear connection which preserves under parallelism the volume form.