An injectivity radius estimate in terms of metric sphere

2015/01/30 by Shicheng Xu, Xu, Shicheng
Mathematics · #53C20 #53C35 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1501.07846

openalex publication_date 2015/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that if a point p in a complete Riemannian manifold is not a cut point of any point whose distance to p is r, then the injectivity radius of p is strictly large than r. As a corollary we give a positive answer to a problem raised by Z. Sun and J. Wan.

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