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arXiv · 2309.11296

On the monotonicity of non-local perimeter of convex bodies

Flavia Giannetti·Giorgio Stefani
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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.

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Flavia Giannetti, Giorgio Stefani. 2023-09-20. On the monotonicity of non-local perimeter of convex bodies. https://arxiv.org/abs/2309.11296

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