A dynamic approach to the Canham problem

Abstract: Motivated by the Canham-Helfrich model for lipid bilayers, the minimization of the Willmore energy among surfaces of given topological type subject to the constraint of fixed isoperimetric ratio has been extensively studied throughout the last decade. In this talk, we consider a dynamical approach by introducing a non-local $L^2$-gradient flow for the Willmore energy, which preserves the isoperimetric ratio. For topological spheres with initial energy below an explicit threshold, we show global existence and convergence to a Helfrich immersion as $t\to\infty$. Our proof relies on a blow-up procedure and a constrained version of the Łojasiewicz--Simon gradient inequality.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometryoptimization and control

Audience: researchers in the topic

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Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php

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