This article is cited in 1 paper

The length of the cut locus on convex surfaces

Liping Yuan^abc, T. Zamfirescu<sup>abde

a</sup> School of Mathematical Sciences, Hebei Normal University, P. R. China
^b Hebei International Joint Research Center for Mathematics and Interdisciplinary Science, P. R. China
^c Hebei Key Laboratory of Computational Mathematics and Applications, P. R. China
^d Fachbereich Mathematik, Technischen Universität Dortmund, Dortmund, Germany
^e Romanian Academy, Bucharest, Romania

Abstract: In this paper, we prove the conjecture stating that, on any closed convex surface, the cut locus of a finite set $M$ with more than two points has length at least half the diameter of the surface.

Keywords: closed convex surface, cut locus, finite set, diameter.

UDC: 515.124

MSC: 53C45, 53C22

Received: 10.04.2023

Language: English

DOI: 10.4213/im9485

 English version: Izvestiya: Mathematics, 2024, 88:3, 590–600

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