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

created by velichkov on 15 Jun 2020
modified on 02 Jan 2023

[BibTeX]

Accepted Paper

Inserted: 15 jun 2020
Last Updated: 2 jan 2023

Journal: Arch. Rat. Mech. Anal.
Year: 2020

ArXiv: 2006.07222 PDF

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 $\lambda$-elastic sets of the solutions Hausdorff converge to the cut locus and the $\lambda$-cut locus of the manifold.