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Minimal surfaces with elastic and partially elastic boundary

Part of: Variational problems in infinite-dimensional spaces Classical differential geometry

Published online by Cambridge University Press:  20 August 2020

Bennett Palmer  and
Álvaro Pámpano
Bennett Palmer
Affiliation:
Department of Mathematics, Idaho State University, Pocatello, ID83209, USA (palmbenn@isu.edu)
Álvaro Pámpano
Affiliation:
Department of Mathematics, University of the Basque Country, Bilbao, Spain (alvaro.pampano@ehu.eus)
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Abstract

We study equilibrium surfaces for an energy which is a linear combination of the area and a second term which measures the bending and twisting of the boundary. Specifically, the twisting energy is given by the twisting of the Darboux frame. This energy is a modification of the Euler–Plateau functional considered by Giomi and Mahadevan (2012, Proc. R. Soc. A 468, 1851–1864), and a natural special case of the Kirchhoff–Plateau energy considered by Biria and Fried (2014, Proc. R. Soc. A 470, 20140368; 2015, Int. J. Eng. Sci. 94, 86–102).

Keywords

bending energiesDarboux frameminimal surfaces

MSC classification

Primary: 58E12: Applications to minimal surfaces (problems in two independent variables)
Secondary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature 53A04: Curves in Euclidean space
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 4 , August 2021 , pp. 1225 - 1246
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Copyright
Copyright © The Author(s) 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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