The length of the cut locus on convex surfaces
- Autores: Yuan L.1, Zamfirescu T.1,2
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Afiliações:
- Hebei Normal University
- Technischen Universität Dortmund
- Edição: Volume 88, Nº 3 (2024)
- Páginas: 192-202
- Seção: Articles
- URL: https://journal-vniispk.ru/1607-0046/article/view/257720
- DOI: https://doi.org/10.4213/im9485
- ID: 257720
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Somente assinantes
Resumo
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.
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Sobre autores
Liping Yuan
Hebei Normal University
Email: Yuan@mail.ru
PhD, Professor
Tudor Zamfirescu
Hebei Normal University; Technischen Universität Dortmund
Autor responsável pela correspondência
Email: Yuan@mail.ru
Bibliografia
- Ю. Д. Бураго, М. Л. Громов, Г. Я. Перельман, “Пространства А. Д. Александрова с ограниченными снизу кривизнами”, УМН, 47:2(284) (1992), 3–51
- J. Itoh, “The length of a cut locus on a surface and Ambrose's problem”, J. Differential Geom., 43:3 (1996), 642–651
- K. Shiohama, M. Tanaka, “Cut loci and distance spheres on Alexandrov surfaces”, Actes de la table ronde de geometrie differentielle (Luminy, 1992), Semin. Congr., 1, Soc. Math. France, Paris, 1996, 531–559
- T. Zamfirescu, “Many endpoints and few interior points of geodesics”, Invent. Math., 69:2 (1982), 253–257
- T. Zamfirescu, “Extreme points of the distance function on convex surfaces”, Trans. Amer. Math. Soc., 350:4 (1998), 1395–1406
- J. J. Hebda, “Metric structure of cut loci in surfaces and Ambrose's problem”, J. Differential Geom., 40:3 (1994), 621–642
- J. Itoh, T. Zamfirescu, “On the length of the cut locus on surfaces”, Stochastic geometry, convex bodies, empirical measures and applications to engineering science (Tropea, 2001), v. II, Rend. Circ. Mat. Palermo (2) Suppl., 70, Circ. Mat. Palermo, Palermo, 2002, 53–58
- J. Itoh, T. Zamfirescu, “On the length of the cut locus for finitely many points”, Adv. Geom., 5:1 (2005), 97–106
- А. Д. Александров, Внутренняя геометрия выпуклых поверхностей, Гостехиздат, М.–Л., 1948, 387 с.
- А. Д. Александров, Внутренняя геометрия выпуклых поверхностей, Гостехиздат, М.–Л., 1948, 387 с.
- Г. Буземан, Выпуклые поверхности, Наука, М., 1964, 238 с.
- T. Zamfirescu, “On the cut locus in Alexandrov spaces and applications to convex surfaces”, Pacific J. Math., 217:2 (2004), 375–386
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