A Reverse Isoperimetric Inequality and its Application to the Gradient Flow of the Helfrich Functional

Simon Blatt

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arXiv · 2009.12273

A Reverse Isoperimetric Inequality and its Application to the Gradient Flow of the Helfrich Functional

Simon Blatt

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Abstract

We prove a quantitative reverse isoperimetric inequality for embedded surfaces with Willmore energy bounded away from $8\pi$. We use this result to analyze the negative $L^2$ gradient flow of the Willmore energy plus a positive multiple of the inclosed volume. We show that initial surfaces of Willmore energy less than $8\pi$ with positive inclosed volume converge to a round point in finite or infinite time.

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Simon Blatt. 2020-09-25. A Reverse Isoperimetric Inequality and its Application to the Gradient Flow of the Helfrich Functional. https://arxiv.org/abs/2009.12273

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