The Willmore flow with prescribed isoperimetric ratio
Analysis of PDEs
2024-02-16 v3 Differential Geometry
Abstract
We introduce a non-local -gradient flow for the Willmore energy of immersed surfaces which preserves the isoperimetric ratio. For spherical initial data with energy below an explicit threshold, we show long-time existence and convergence to a Helfrich immersion. This is in sharp contrast to the locally constrained flow, where finite time singularities occur.
Keywords
Cite
@article{arxiv.2106.02579,
title = {The Willmore flow with prescribed isoperimetric ratio},
author = {Fabian Rupp},
journal= {arXiv preprint arXiv:2106.02579},
year = {2024}
}
Comments
Final version. 30 pages, 1 figure. To appear in Comm. Partial Differential Equations