Email this article On the Toroidal Surfaces of Revolution with Constant Mean Curvatures
- Authors: Ilgisonis V.I.1,2,3, Skovoroda A.A.1, Sorokina E.A.1,2,3
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Affiliations:
- National Research Center Kurchatov Institute
- Peoples’ Friendship University of Russia (RUDN University)
- National Research Nuclear University MEPhI
- Issue: Vol 80, No 7 (2017)
- Pages: 1307-1312
- Section: Article
- URL: https://journal-vniispk.ru/1063-7788/article/view/192999
- DOI: https://doi.org/10.1134/S1063778817070067
- ID: 192999
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Abstract
It is shown that the surface with a constant mean curvature encloses the extremal volume among all toroidal surfaces of given area. The exact solution for the corresponding variational problem is derived, and its parametric analysis is performed in the limits of high and small mean curvatures. An absence of smooth torus with constant mean curvature is proved, and the extremal surface is demonstrated to have at least one edge located on the outer side of the torus.
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About the authors
V. I. Ilgisonis
National Research Center Kurchatov Institute; Peoples’ Friendship University of Russia (RUDN University); National Research Nuclear University MEPhI
Email: Skovoroda_AA@nrcki.ru
Russian Federation, Moscow; Moscow; Moscow
A. A. Skovoroda
National Research Center Kurchatov Institute
Author for correspondence.
Email: Skovoroda_AA@nrcki.ru
Russian Federation, Moscow
E. A. Sorokina
National Research Center Kurchatov Institute; Peoples’ Friendship University of Russia (RUDN University); National Research Nuclear University MEPhI
Email: Skovoroda_AA@nrcki.ru
Russian Federation, Moscow; Moscow; Moscow
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