Gradient flow dynamics for cell membranes in the Canham-Helfrich model
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909287036485632 |
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| author | Rupp, Fabian Scharrer, Christian Schlierf, Manuel |
| author_facet | Rupp, Fabian Scharrer, Christian Schlierf, Manuel |
| contents | 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 a spontaneous curvature and the conservation of surface area and enclosed volume. Using a recently discovered multiplicity inequality, we prove global existence and convergence of smooth solutions for spheres and axisymmetric tori, provided the initial energy lies below explicit thresholds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_07493 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gradient flow dynamics for cell membranes in the Canham-Helfrich model Rupp, Fabian Scharrer, Christian Schlierf, Manuel Analysis of PDEs Differential Geometry 53E40 (primary), 35B40, 49Q10 (secondary) 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 a spontaneous curvature and the conservation of surface area and enclosed volume. Using a recently discovered multiplicity inequality, we prove global existence and convergence of smooth solutions for spheres and axisymmetric tori, provided the initial energy lies below explicit thresholds. |
| title | Gradient flow dynamics for cell membranes in the Canham-Helfrich model |
| topic | Analysis of PDEs Differential Geometry 53E40 (primary), 35B40, 49Q10 (secondary) |
| url | https://arxiv.org/abs/2408.07493 |