On the monotonicity of non-local perimeter of convex bodies
DOI:
https://doi.org/10.12775/TMNA.2024.019Keywords
Convex body, non-local perimeter, monotonicity, Hausdorff distance, Schwartz symmetrizationAbstract
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.References
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