Work

On the Minimization of the Willmore Energy Under a Constraint on Total Mean Curvature and Area

Year: 2025

Type: article

Abstract: Motivated by a model for lipid bilayer cell membranes, we study the minimization of the Willmore functional in the class of oriented closed surfaces with prescribed total mean curvature, prescribed area, and prescribed genus. Adapting methods previously developed by Keller–Mondino–Rivière, Bauer–Kuwert, and Ndiaye–Schätzle, we prove the existence of smooth minimizers for a large class of constraints. Moreover, we analyze the asymptotic behaviour of the energy profile close to the unit sphere and consider the total mean curvature of axisymmetric surfaces.

Source: Archive for Rational Mechanics and Analysis

DOI: 10.1007/s00205-025-02087-y

Authors: Christian Scharrer, Alexander West

Institution: University of Bonn

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Rheinische Friedrich-Wilhelms-Universität Bonn