Open Access
May 2014 Confined structures of least bending energy
Stefan Müller, Matthias Röger
J. Differential Geom. 97(1): 109-139 (May 2014). DOI: 10.4310/jdg/1404912105


In this paper we study a constrained minimization problem for the Willmore functional. For prescribed surface area, we consider smooth embeddings of the sphere into the unit ball. We evaluate the dependence of the the minimal Willmore energy of such surfaces on the prescribed surface area and prove corresponding upper and lower bounds. Interesting features arise when the prescribed surface area just exceeds the surface area of the unit sphere. We show that (almost) minimizing surfaces cannot be a $C^2$-small perturbation of the sphere. Indeed, they have to be nonconvex and there is a sharp increase in Willmore energy with a square root rate with respect to the increase in surface area.


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Stefan Müller. Matthias Röger. "Confined structures of least bending energy." J. Differential Geom. 97 (1) 109 - 139, May 2014.


Published: May 2014
First available in Project Euclid: 9 July 2014

zbMATH: 1305.60089
MathSciNet: MR3229052
Digital Object Identifier: 10.4310/jdg/1404912105

Rights: Copyright © 2014 Lehigh University

Vol.97 • No. 1 • May 2014
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