A singular integral identity for surface measure
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917948083404800 |
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| author | Bushling, Ryan E. G. |
| author_facet | Bushling, Ryan E. G. |
| contents | We prove that the integral of a certain Riesz-type kernel over $(n-1)$-rectifiable sets in $\mathbb{R}^n$ is constant, from which a formula for surface measure immediately follows. Geometric interpretations are given, and the solution to a geometric variational problem characterizing convex domains follows as a corollary, strengthening a recent inequality of Steinerberger. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_04930 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A singular integral identity for surface measure Bushling, Ryan E. G. Classical Analysis and ODEs Primary 28A75, 53A07, Secondary 51M16, 52A38 We prove that the integral of a certain Riesz-type kernel over $(n-1)$-rectifiable sets in $\mathbb{R}^n$ is constant, from which a formula for surface measure immediately follows. Geometric interpretations are given, and the solution to a geometric variational problem characterizing convex domains follows as a corollary, strengthening a recent inequality of Steinerberger. |
| title | A singular integral identity for surface measure |
| topic | Classical Analysis and ODEs Primary 28A75, 53A07, Secondary 51M16, 52A38 |
| url | https://arxiv.org/abs/2304.04930 |