A singular integral identity for surface measure
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...
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | 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. |
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| DOI: | 10.48550/arxiv.2304.04930 |