Laplacian of the distance function on the cut locus on a riemannian manifold

Abstract

We show that, on a smooth riemannian manifold, the laplacian of the distance function to a point $b$ is $-\infty$ in the sense of barriers, at every point of the cut locus with respect to $b$.

References in corpus (2)

• Hamilton-Jacobi Equations and Distance Functions on Riemannian Manifolds
• On the Distributional Hessian of the Distance Function