A Bound on the Number of Endpoints of the Cut Locus
Robert M. Sinclair, Minoru Tanaka · LMS Journal of Computation and Mathematics · 2006
Abstract We provide strong experimental evidence for an upper bound on the number of endpoints of the cut locus from a point on a 2-surface of revolution. This bound is equal to the minimal number of intervals of monotone non-increasing or non-decreasing Gaussian curvature along one meridian from one pole to the other.