Willmore minimizers with prescribed isoperimetric ratio
Johannes Schygulla
TL;DR
This paper studies the minimization of the Willmore functional for embedded spheres in three-dimensional space with a fixed isoperimetric ratio, inspired by models of elastic cell membranes.
Contribution
It introduces a variational problem for Willmore minimizers with a prescribed isoperimetric ratio, providing new insights into their geometric properties.
Findings
Existence of minimizers under the given constraints
Characterization of the minimizers' geometric features
Potential applications to biological membrane modeling
Abstract
Motivated by a simple model for elastic cell membranes, we minimize the Willmore functional among two-dimensional spheres embedded in R^3 with prescribed isoperimetric ratio.
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