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VOL. 17 | 2016 Axially Symmetric Willmore Surfaces Determined by Quadratures
Vassil M. Vassilev, Peter A. Djondjorov, Mariana Ts. Hadzhilazova, Ivaïlo M. Mladenov

Editor(s) Ivaïlo M. Mladenov, Guowu Meng, Akira Yoshioka

Abstract

The work is concerned with a special family of axially symmetric surfaces providing local extrema to the so-called Willmore functional, which assigns to each surface its total squared mean curvature. The components of the position vector of the profile curves of the regarded Willmore surfaces satisfy a system of first-order ordinary differential equations. The solutions of this system are expressed by quadratures in terms of the tangent angle and, in this way, the corresponding Willmore surfaces are determined.

Information

Published: 1 January 2016
First available in Project Euclid: 15 December 2015

zbMATH: 1346.53010
MathSciNet: MR3445442

Digital Object Identifier: 10.7546/giq-17-2016-369-378

Rights: Copyright © 2016 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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