The cut loci on ellipsoids and certain Liouville manifolds

2009/04/30 by Jin‐ichi Itoh, Itoh, Jin-ichi, Kazuyoshi Kiyohara +1
Mathematics · #53C22 #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.0904.4743

openalex publication_date 2009/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that some riemannian manifolds diffeomorphic to the sphere have the property that the cut loci of general points are smoothly embedded closed disks of codimension one. Ellipsoids with distinct axes are typical examples of such manifolds.

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