Geodesic
The length of the cut locus on convex surfaces
Izvestiya. Mathematics , Tome 88 (2024) no. 3, pp. 590-600

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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     author = {Liping Yuan and T. Zamfirescu},
     title = {The length of the cut locus on convex surfaces},
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Liping Yuan; T. Zamfirescu. The length of the cut locus on convex surfaces. Izvestiya. Mathematics , Tome 88 (2024) no. 3, pp. 590-600. http://geodesic.mathdoc.fr/item/IM2_2024_88_3_a6/