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

DOI10.1007/s00526-012-0553-9zbMath1278.49049arXiv1202.1979OpenAlexW2095225578MaRDI QIDQ376611

Rustum Choksi, Marco Veneroni

Publication date: 5 November 2013

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.1979

zbMATH Keywords

global minimizersshape analysisbiomembranesCanham-Helfrich functional

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Applications of global differential geometry to the sciences (53C80) Optimization of shapes other than minimal surfaces (49Q10) Variational problems in infinite-dimensional spaces (58E99)

Related Items (15)

Embedded Delaunay tori and their Willmore energy ⋮ Existence of varifold minimizers for the multiphase Canham-Helfrich functional ⋮ The tension determination problem for an inextensible interface in 2D Stokes flow ⋮ Li-Yau inequalities for the Helfrich functional and applications ⋮ Variational models for the interaction of surfactants with curvature – existence and regularity of minimizers in the case of flexible curves ⋮ Lower semicontinuity for the Helfrich problem ⋮ On \(p\)-Willmore disks with boundary energies ⋮ Numerical shape optimization of the Canham-Helfrich-Evans bending energy ⋮ Direct minimization of the Canham-Helfrich energy on generalized Gauss graphs ⋮ A Helfrich functional for compact surfaces in ⋮ Boundary value problems for a special Helfrich functional for surfaces of revolution: existence and asymptotic behaviour ⋮ Existence and regularity of spheres minimising the Canham-Helfrich energy ⋮ Phase field models for thin elastic structures with topological constraint ⋮ The Helfrich boundary value problem ⋮ Minimisers of Helfrich functional for surfaces of revolution

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