Every point in a Riemmanian manifold is critical

2014/08/20 by Fernando Galaz‐García, Fernando Galaz-Garcia, Luis Guijarro +2
Computer Science · Mathematics · #53C20 #53C22 #Advanced Mathematical Modeling in Engineering #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #math.DG #math.MG #msc:53C20 #msc:53C22

paper · pdf · doi:10.48550/arxiv.1408.4777

7 pages, 2 figures. Minor changes. Accepted for publication in Calculus of Variations and Partial Differential Equations

openalex publication_date 2014/08/20 · arxiv created 2015/03/17 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for any point p in a closed Riemannian manifold M, there exists at least one point q∈ M such that p is critical for the distance function from q. We also show that such a point q cannot always be reached with geodesic loops based at q with midpoint p.

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