Closed geodesics with Lipschitz obstacle
It is considered a different kind of nonsmooth subset of \(\mathbb{R}^n\) with Lipschitz boundary. A new definition for geodesics on a general subset of \(\mathbb{R}^n\) is proposed and their basic property is showed. This definition is related to the nonsmooth critical point theory, presented below. The main result of this paper is a proof of the existence of at least one nonconstant closed geodesic in certain situations.
scientific article; zbMATH DE number 1295278
scientific article