Description

• Title:
  On the monotonicity of non-local perimeter of convex bodies
• Creator:
  Giannetti, Flavia;
  Stefani, Giorgio
• Description:
  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.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2024 Flavia Giannetti, Giorgio Stefani
• Date:
  2024.09.25
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 64, No 2 (December 2024); 693 - 710;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/55394/39876 ;https://apcz.umk.pl/TMNA/article/view/55394/39877
• Subject:
  Convex body;
  non-local perimeter;
  monotonicity;
  Hausdorff distance;
  Schwartz symmetrization;
  Primary: 52A20;
  Secondary: 52A40
• Identifier: https://apcz.umk.pl/TMNA/article/view/55394
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other