Complete Finsler manifolds in presence of strictly convex functions

Abstract:  After introducing the notion of a Finsler manifold, a smooth manifold with a smoothly varying family of Minkowski norms, we will discuss some of its properties in the presence of a strictly convex function. 

A well known theorem of E. Cartan states that every compact isometry group action on a Hadamard manifold has a fixed point. Yamaguchi extended this theorem and proved that if a Riemannian manifold M admits a strictly convex function with minimum, then each compact subgroup of isometry group of M has a common fixed point. Cartan's theorem follows from the fact that the distance function to every point on M is strictly convex. In this talk, we discuss a generalized version of Yamaguchi result for Finsler manifolds.