Gradient Flow Dynamics for Cell Membranes in the Canham–Helfrich Model
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.
Fields of Study & Subjects
Mathematical and Theoretical Epidemiology and Ecology Models
Nonlinear Dynamics and Pattern Formation
Publication details
- Journal / source
- Archive for Rational Mechanics and Analysis
- Publisher
- Springer Science and Business Media LLC
- Volume
- 250
- Issue
- 5
- Pages
- 81–81
- Publication date
- 24 August 2026
- Language
- EN