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Gradient Flow Dynamics for Cell Membranes in the Canham-Helfrich Model
Fabian Rupp1, Christian Scharrer2, Manuel Schlierf3
1Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.
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.
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