Work

Gradient Flow Dynamics for Cell Membranes in the Canham–Helfrich Model

Year: 2026

Type: article

Abstract: The most energetically efficient way that a deformed red blood cell regains equilibrium is mathematically described by the gradient flow of the Canham-Helfrich functional, including a spontaneous curvature and the conservation of surface area and enclosed volume. Using a recently discovered multiplicity inequality, we prove the global existence and convergence of smooth solutions for spheres and axisymmetric tori, provided that the initial energy lies below explicit thresholds.

Source: Archive for Rational Mechanics and Analysis

DOI: 10.1007/s00205-026-02235-y

Authors: Fabian Rupp, Christian Scharrer, Manuel Schlierf

Institutions: University of Vienna, University of Bonn, University of Salzburg

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: Austrian Science Fund