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