Weak geodesics on prox-regular subsets of Riemannian manifolds

2022/05/18 by Ferrera, Juan, Pouryayevali, Mohamad R., Radmanesh, Hajar
#49J52 #58C06 #58C20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2205.08757

Abstract

We give a definition of weak geodesics on prox-regular subsets of Riemannian manifolds as continuous curves with some weak regularities. Then obtaining a suitable Lipschitz constant of the projection map, we characterize weak geodesics on a prox-regular set with assigned end points as viscosity critical points of the energy functional.

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