Abstract: Motivated by a model for lipid bilayers, the minimization of the Willmore energy subject to the constraint of fixed isoperimetric ratio has been extensively studied throughout the last decade. In this talk, we present a time-dependent approach by introducing a non-local L2-gradient flow for the problem. For topological spheres with initial energy below an explicit threshold, we show global existence and convergence to a Helfrich immersion as time goes to infinity. Our proof relies on a blow-up procedure and a suitable version of the Łojasiewicz–Simon gradient inequality.
Deforming cell membranes towards their equilibrium — A gradient flow for the Canham–Helfrich model
15.12.2021 14:00 - 14:45
Organiser:
SFB 65, DK
Location:
Zoom Meeting