Hausdorff Stability of the Cut Locus Under $C^2$-Perturbations of the Metric

Aritra Bhowmick, Jin-ichi Itoh, Sachchidanand Prasad

In this article, we prove the stability with respect to the Hausdorff metric $d_H$ of the cut locus $\mathrm{Cut}(p,\mathfrak{g})$ of a point $p$ in a compact Riemannian manifold…