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arXiv · 2401.11939

A new proof of the Willmore inequality via a divergence inequality

Carla Cederbaum·Anabel Miehe
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Abstract

We present a new proof of the Willmore inequality for an arbitrary bounded domain $\Omega\subset\mathbb{R}^{n}$ with smooth boundary. Our proof is based on a parametric geometric inequality involving the electrostatic potential for the domain $\Omega$; this geometric inequality is derived from a geometric differential inequality in divergence form. Our parametric geometric inequality also allows us to give new proofs of the quantitative Willmore-type and the weighted Minkowski inequalities by Agostiniani and Mazzieri.

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Carla Cederbaum, Anabel Miehe. 2024-01-22. A new proof of the Willmore inequality via a divergence inequality. https://doi.org/10.1090/tran%2F9445

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