The Euler-Helfrich functional

DOI10.1007/s00526-022-02188-6zbMath1490.49030arXiv2107.12500OpenAlexW3184060579WikidataQ114017980 ScholiaQ114017980MaRDI QIDQ2117983

Bennett Palmer, Álvaro Pámpano

Publication date: 22 March 2022

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

Full work available at URL: https://arxiv.org/abs/2107.12500

zbMATH Keywords

critical pointsminimal surfacesEuler-Hilfreich energy

Mathematics Subject Classification ID

Optimization of shapes other than minimal surfaces (49Q10) Surfaces in Euclidean and related spaces (53A05) Curves in Euclidean and related spaces (53A04)

Related Items (3)

Symmetry breaking bifurcation of membranes with boundary ⋮ A relation between cylindrical critical points of Willmore-type energies, weighted areas and vertical potential energies ⋮ On \(p\)-Willmore disks with boundary energies

Cites Work

• Unnamed Item
• Unnamed Item
• Geometry of membranes
• Elastic curves with constant curvature at rest in the hyperbolic plane
• Multiple integrals in the calculus of variations
• The conformal Gauss map and the stability of Willmore surfaces
• Invariant singular minimal surfaces
• Existence and regularity of spheres minimising the Canham-Helfrich energy
• Minimizing configurations for elastic surface energies with elastic boundaries
• Boundary value problems for a special Helfrich functional for surfaces of revolution: existence and asymptotic behaviour
• On a variational problem for soap films with gravity and partially free boundary
• Symmetry of stationary hypersurfaces in hyperbolic space
• Uniqueness theorems for Willmore surfaces with fixed and free boundaries
• A geometric theory on the elasticity of bio-membranes
• Geometry and stability of bubbles with gravity

This page was built for publication: The Euler-Helfrich functional