A new proof of the Willmore inequality via a divergence inequality
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913975204052992 |
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| author | Cederbaum, Carla Miehe, Anabel |
| author_facet | Cederbaum, Carla Miehe, Anabel |
| contents | We present a new proof of the Willmore inequality for an arbitrary bounded domain $Ω\subset\mathbb{R}^{n}$ with smooth boundary. Our proof is based on a parametric geometric inequality involving the electrostatic potential for the domain $Ω$; 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_11939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new proof of the Willmore inequality via a divergence inequality Cederbaum, Carla Miehe, Anabel Analysis of PDEs Differential Geometry 31B05, 53C99, 35A16 We present a new proof of the Willmore inequality for an arbitrary bounded domain $Ω\subset\mathbb{R}^{n}$ with smooth boundary. Our proof is based on a parametric geometric inequality involving the electrostatic potential for the domain $Ω$; 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. |
| title | A new proof of the Willmore inequality via a divergence inequality |
| topic | Analysis of PDEs Differential Geometry 31B05, 53C99, 35A16 |
| url | https://arxiv.org/abs/2401.11939 |