Symmetry breaking bifurcation of membranes with boundary

DOI10.1016/j.na.2023.113393zbMath1527.35039arXiv2206.10971MaRDI QIDQ6086070

Bennett Palmer, Álvaro Pámpano

Publication date: 9 November 2023

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.10971

zbMATH Keywords

symmetry breakingHelfrich energyCrandall and Rabinowitz-type bifurcation

Mathematics Subject Classification ID

Membranes (74K15) Optimization of shapes other than minimal surfaces (49Q10) Surfaces in Euclidean and related spaces (53A05) Bifurcations in context of PDEs (35B32) Semilinear elliptic equations (35J61)

Cites Work

• Radially symmetric solutions of an anisotropic mean curvature equation modeling the corneal shape
• Geometry of membranes
• Deformation and stability of surfaces with constant mean curvature
• Stability and bifurcation for surfaces with constant mean curvature
• Minimizing configurations for elastic surface energies with elastic boundaries
• The Euler-Helfrich functional
• Bifurcation from simple eigenvalues
• Axial-symmetry breaking in constrained membranes
• Stresses in lipid membranes
• A geometric theory on the elasticity of bio-membranes

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