Cut locus on compact manifolds and uniform semiconcavity estimates for a variational inequality

2020/06/12 by Générau, François, Oudet, Edouard, Velichkov, Bozhidar · 1 citation
#35R35 #53C21 #53C22 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.07222

Abstract

We study a family of gradient obstacle problems on a compact Riemannian manifold. We prove that the solutions of these free boundary problems are uniformly semiconcave and, as a consequence, we obtain some fine convergence results for the solutions and their free boundaries. Precisely, we show that the elastic and the λ-elastic sets of the solutions Hausdorff converge to the cut locus and the λ-cut locus of the manifold.

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• Zero Probability of the Cut Locus of a Fréchet Mean on a Riemannian Manifold

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