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

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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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Authors and Affiliations

  1. Department of Mathematics and Statistics, McGill University, Montreal, QC, Canada

    Rustum Choksi & Marco Veneroni

  2. Dipartimento di Matematica Felice Casorati, Università di Pavia, Pavia, Italy

    Marco Veneroni

Authors
  1. Rustum Choksi
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  2. Marco Veneroni
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Correspondence to Marco Veneroni.

Additional information

Communicated by L. Ambrosio.

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Choksi, R., Veneroni, M. Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case. Calc. Var. 48, 337–366 (2013). https://doi.org/10.1007/s00526-012-0553-9

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  • DOI: https://doi.org/10.1007/s00526-012-0553-9

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