Author

Tong-Ou Yang

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Preprint Sep 2026

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

We prove sharp volume bounds (up to dimensional constants) for the $\delta$-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 shar...

Xiang-Hong Chen, Tong-Ou Yang · 0 citations

Preprint Sep 2026

Level set estimates for strictly convex and hyperbolic functions

In this note, we prove uniform upper bounds for the volume of the level set $$\{x\in\Omega: c\le f(x)0,$$ for strictly convex and hyperbolic functions $f$ defined on a convex domain $\Omega\subset\mathbb{R}^n$ ($n\ge 2$). In particular, under a Hessian lower bound $D^2f\ge I_n$, we obtain the sharp volume bound $$|S^{n...

Xiang-Hong Chen, Tong-Ou Yang · 1 citation