On Perimeters and Volumes of Fattened Sets

In this paper we analyze the shape of fattened sets; given a compact set C⊂RN let Cr be its r-fattened set; we prove a general bound rP(Cr)≤NL({Cr∖C}) between the perimeter of Cr and the Lebesgue measure of Cr∖C. We provide two proofs: one elementary and one based on Geometric Measure Theory. Note t...

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Bibliographic Details
Main Author: Andrea C. G. Mennucci
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2019/8283496