CONVERGENCE OF AN APPROXIMATION FOR ROTATIONALLY SYMMETRIC TWO-PHASE LIPID BILAYER MEMBRANES

DOI10.1093/qmath/hau027zbMath1326.49020arXiv1603.05231OpenAlexW2124957860MaRDI QIDQ5247453

Michael Helmers

Publication date: 24 April 2015

Published in: The Quarterly Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.05231

zbMATH Keywords

\(\Gamma\)-limitdiffuse interface approximationtwo-phase lipid bilayer membranes

Mathematics Subject Classification ID

Regularity of solutions in optimal control (49N60) Biochemistry, molecular biology (92C40) Methods involving semicontinuity and convergence; relaxation (49J45) Applications of global differential geometry to the sciences (53C80) Optimization of shapes other than minimal surfaces (49Q10)

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On the sharp interface limit of a phase field model for near spherical two phase biomembranes ⋮ Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case ⋮ Existence of varifold minimizers for the multiphase Canham-Helfrich functional ⋮ Phase separation on varying surfaces and convergence of diffuse interface approximations ⋮ Variational models for the interaction of surfactants with curvature – existence and regularity of minimizers in the case of flexible curves ⋮ Direct minimization of the Canham-Helfrich energy on generalized Gauss graphs ⋮ Small deformations of spherical biomembranes ⋮ Gradient flow dynamics of two-phase biomembranes: Sharp interface variational formulation and finite element approximation ⋮ Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds

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