Cut Locus (Riemannian Manifold)

Cut Locus (Riemannian Manifold)

In Riemannian geometry, the cut locus of a point in a manifold is roughly the set of all other points for which there are multiple minimizing geodesics connecting them from, but it may contain additional points where the minimizing geodesic is unique, under certain circumstances. The distance function from p is a smooth function except at the point p itself and the cut locus.