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arXiv · 2106.02579

The Willmore flow with prescribed isoperimetric ratio

Fabian Rupp
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Abstract

We introduce a non-local $L^2$-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.

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Fabian Rupp. 2021-06-04. The Willmore flow with prescribed isoperimetric ratio. https://doi.org/10.1080/03605302.2024.2302377

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