Minimal geodesics and integrable behavior in geodesic flows

Abstract

In this survey article we gather classical as well as recent results on minimal geodesics of Riemannian or Finsler metrics, giving special attention to the two-dimensional case. Moreover, we present open problems together with some first ideas as to the solutions.

84 pages, 9 figures

References in corpus (5)

• Lecture notes on Mather's theory for Lagrangian systems
• Topological entropy of minimal geodesics and volume growth on surfaces
• Uniqueness of shortest closed geodesics for generic Finsler metrics
• An entropic characterization of the flat metrics on the two torus
• On the ergodicity of geodesic flows on surfaces of nonpositive curvature