Liping Yuan, T. Zamfirescu, “The length of the cut locus on convex surfaces”, Изв. РАН. Сер. матем., 2024, том 88, выпуск 3,страницы 192

The length of the cut locus on convex surfaces

Liping Yuan^abc, T. Zamfirescu^abde

^a 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

Аннотация: 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.

Ключевые слова: closed convex surface, cut locus, finite set, diameter.

УДК: 515.124

MSC: 53C45, 53C22

Поступило в редакцию: 10.04.2023

Язык публикации: английский

DOI: 10.4213/im9485