Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case

Details Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case

2012-02-09

arxiv.org/abs/1202.1979v1

Mathematics

Analysis of PDEs

30 pages, 6 figures

Scientific paper

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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