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math.AP2024
Gradient flow dynamics for cell membranes in the Canham-Helfrich model
Fabian Rupp, Christian Scharrer, Manuel Schlierf
The energetically most efficient way how a deformed red blood cell regains equilibrium is mathematically described by the gradient flow of the Canham-Helfrich functional, including…
math.AP2024
Introducing spontaneous curvature to the Helfrich flow: Singularities and convergence
Manuel Schlierf
While there are various results on the long-time behavior of the Willmore flow, the Helfrich flow with non-zero spontaneous curvature as its natural generalization is not yet well-…
math.AP2024
Global existence for the Willmore flow with boundary via Simon's Li-Yau inequality
Manuel Schlierf
It is well-known that the Willmore flow of closed spherical immersions exists globally in time and converges if the initial datum has Willmore energy below - exactly the Li-Ya…