Calculus of Variations and Geometric Measure Theory

R. Choksi - M. Morandotti - M. Veneroni

Global minimizers for axisymmetric multiphase membranes

created by morandott on 30 Apr 2012
modified on 24 Apr 2014


Published Paper

Inserted: 30 apr 2012
Last Updated: 24 apr 2014

Volume: 19
Pages: 1014–1029
Year: 2013
Doi: 10.1051/cocv/2012042


We consider a Canham-Helfrich-type variational problem de ned over closed surfaces enclosing a xed volume and having xed 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 $[7]$ and prove existence of a global minimizer.

Keywords: Helfrich functional, biomembranes, global minimizers, axisymmetric surfaces, multicomponent vesicle