Submitted Paper
Inserted: 20 sep 2023
Last Updated: 20 sep 2023
Year: 2023
Abstract:
Under mild assumptions on the kernel $K\ge0$, the non-local $K$-perimeter $P_K$ satisfies the monotonicity property on nested convex bodies, i.e., if $A\subset B\subset\mathbb{R}^n$ are two convex bodies, then $P_K(A)\le P_K(B)$. In this note, we prove quantitative lower bounds on the difference of the $K$-perimeters of $A$ and $B$ in terms of their Hausdorff distance, provided that $K$ satisfies suitable symmetry properties.
Keywords: Hausdorff distance, monotonicity, convex body, non-local perimeter, Schwartz symmetrization
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