Regarding the Euler–Plateau problem with elastic modulus

Anthony Gruber, Álvaro Pámpano, Magdalena Toda

Research output: Contribution to journalArticlepeer-review


We study equilibrium configurations for the Euler–Plateau energy with elastic modulus, which couples an energy functional of Euler–Plateau type with a total curvature term often present in models for the free energy of biomembranes. It is shown that the potential minimizers of this energy are highly dependent on the choice of physical rigidity parameters, and that the area of critical surfaces can be computed entirely from their boundary data. When the elastic modulus does not vanish, it is shown that axially symmetric critical immersions and critical immersions of disk type are necessarily planar domains bounded by area-constrained elasticae. The cases of topological genus zero with multiple boundary components and unrestricted genus with control on the geodesic torsion are also discussed, and sufficient conditions are given which establish the same conclusion in these cases.

Original languageEnglish
Pages (from-to)2263-2283
Number of pages21
JournalAnnali di Matematica Pura ed Applicata
Issue number5
StatePublished - Oct 2021


  • Area-constrained elasticae
  • Euler–Plateau energy
  • Minimal surfaces


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