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arXiv · 2609.39059

Sharp volume bounds for BRK-type sets of surfaces of revolution

Xianghong Chen·Tongou Yang
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Abstract

We prove sharp volume bounds (up to dimensional constants) for the $δ$-neighbourhoods of a general family of Besicovitch-Rado-Kinney (BRK) type sets associated with surfaces of revolution in $\mathbb R^n$, $n\ge 3$, which, in particular, include spheres, elliptic paraboloids, and cones. As a result, we obtain sharp $L^{p}$-$L^q$ bounds for their associated Wolff-type maximal operators for all $1\le p,q\le \infty$. In $\mathbb R^3$, it is worth noting that our result necessitates a variant of Sogge's cinematic curvature condition.

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Xianghong Chen, Tongou Yang. 2026-09-30. Sharp volume bounds for BRK-type sets of surfaces of revolution. https://arxiv.org/abs/2609.39059

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