Calculus of Variations and Geometric Measure Theory
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V. Julin - G. Saracco

Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants

created by saracco on 24 Mar 2020
modified on 31 Aug 2021


Published Paper

Inserted: 24 mar 2020
Last Updated: 31 aug 2021

Journal: Ann. Fenn. Math.
Volume: 46
Number: 2
Pages: 1071--1087
Year: 2021
Doi: 10.5186/aasfm.2021.4666

ArXiv: 2003.10930 PDF


We provide a quantitative lower bound to the Cheeger constant of a set $\Omega$ in both the Euclidean and the Gaussian settings in terms of suitable asymmetry indexes. We provide examples which show that these quantitative estimates are sharp.

Keywords: Cheeger sets, Cheeger constant, quantitative inequalities


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