Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case |
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Authors: | Rustum Choksi Marco Veneroni |
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Institution: | 1. Department of Mathematics and Statistics, McGill University, Montreal, QC, Canada 2. Dipartimento di Matematica Felice Casorati, Università di Pavia, Pavia, Italy
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Abstract: | Since the pioneering work of Canham and Helfrich, variational formulations involving curvature-dependent functionals, like the classical Willmore functional, have proven useful for shape analysis of biomembranes. We address minimizers of the Canham–Helfrich functional defined over closed surfaces enclosing a fixed volume and having fixed surface area. By restricting attention to axisymmetric surfaces, we prove the existence of global minimizers. |
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