Year: 2026
Type: preprint
Abstract: For $n\geq 2$ and $1<p<n$, Ludwig-Xiao-Zhang \cite{LXYZ} asked whether the $L_p$-integral affine surface area of every convex body containing the origin in its interior is bounded above by the ball-normalized multiple of \(L_p\)-variational capacity, and whether the analogous analytic inequality holds for $L_p$-convexified level sets. We answer both questions negatively.
Source: arXiv (Cornell University)
Authors: Yibin Feng, Ding Zhang
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204224493