Cut Locus on a Compact Riemannian Surface
Kecheng Zhou · Huadong Shifan Daxue xuebao. Ziran kexue ban · 1984
Cut locus wag first introduced by Poincare for compact surfaces of positive curvature,and was elaborated by, among others, B.Myers.B.Myers discussed the cut locus for a Riemannian surface in [1], which is an article of wide influence.With a new method,an improvement on Myers' article is presented here, to prove that on a compact Riemannian surface, as a out point, the order of a point in a cut locus is equal to its order as a vertex of this simplicial complex.