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A Singular Integral Identity for Surface Measure

Ryan Bushling, University of Washington
Thursday, April 6, 2023 - 12:30pm to 1:20pm
PDL C-401

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 a recent inequality of Steinerberger characterizing convex domains follows as a corollary.