We consider a Canham-Helfrich-type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the Canham-Helfrich energy, in which the bending rigidities and spontaneous curvatures are now phase-dependent, and a line tension penalization for the phase interfaces. By restricting attention to axisymmetric surfaces and phase distributions, we extend our previous results for a single phase (R. Choksi and M. Veneroni, Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case. Calc. Var. Partial Differential Equations, 2012. DOI: 10.1007/s00526-012-0553-9) and prove existence of a global minimizer.
Global minimizers for axisymmetric multiphase membranes
VENERONI, MARCO
2013-01-01
Abstract
We consider a Canham-Helfrich-type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the Canham-Helfrich energy, in which the bending rigidities and spontaneous curvatures are now phase-dependent, and a line tension penalization for the phase interfaces. By restricting attention to axisymmetric surfaces and phase distributions, we extend our previous results for a single phase (R. Choksi and M. Veneroni, Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case. Calc. Var. Partial Differential Equations, 2012. DOI: 10.1007/s00526-012-0553-9) and prove existence of a global minimizer.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
