Local minimality of weak geodesics on prox-regular subsets of Riemannian manifolds

2023/11/22 by Ferrera, Juan, Pouryayevali, Mohamad R., Radmanesh, Hajar
#49J52 #58C06 #58C20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.13256

Abstract

In this paper we prove that every locally minimizing curve with constant speed in a prox-regular subset of a Riemannian manifold is a weak geodesic. Moreover, it is shown that under certain assumptions, every weak geodesic is locally minimizing. Furthermore a notion of closed weak geodesics on prox-regular sets is introduced and a characterization of these curves as nonsmooth critical points of the energy functional is presented.

Related

• Weak geodesics on prox-regular subsets of Riemannian manifolds
• Minimizing curves in prox-regular subsets of Riemannian manifolds
• Minimizing Closed Geodesics via Critical Points of the Uniform Energy
• Locally extremal geodesic loops on Riemannian manifold
• Nonconvex weak sharp minima on Riemannian manifolds