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arXiv · 2011.14904

A strict inequality for the minimisation of the Willmore functional under isoperimetric constraint

Andrea Mondino·Christian Scharrer
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Abstract

Inspired by previous work of Kusner and Bauer-Kuwert, we prove a strict inequality between the Willmore energies of two surfaces and their connected sum in the context of isoperimetric constraints. Building on previous work by Keller-Mondino-Rivi\`ere, our strict inequality leads to existence of minimisers for the isoperimetric constrained Willmore problem in every genus, provided the minimal energy lies strictly below $8\pi$. Besides the geometric interest, such a minimisation problem has been studied in the literature as a simplified model in the theory of lipid bilayer cell membranes.

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BibTeXRIS

Andrea Mondino, Christian Scharrer. 2020-11-30. A strict inequality for the minimisation of the Willmore functional under isoperimetric constraint. https://doi.org/10.1515/acv-2021-0002

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