A new proof of the Willmore inequality via a divergence inequality
| Autor: | Cederbaum, Carla, Miehe, Anabel |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 26 pages, 1 figure. Comments very welcome; erroneous application of Morse--Sard theorem corrected |
| Databáze: | arXiv |
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