Calculus of Variations and Geometric Measure Theory

V. Julin - G. Saracco

Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants

created by saracco on 24 Mar 2020
modified on 06 Nov 2023


Published Paper

Inserted: 24 mar 2020
Last Updated: 6 nov 2023

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

ArXiv: 2003.10930 PDF

In the published paper in the definition (2.2) of the index $\zeta(\Omega)$ the rescaling factor is missing (as otherwise the quantitative inequality (2.5) would be false as written). Consequently, in the proof of Theorem 2.1 and in the following example several renormalization constants are missing. The preprint contains the correct definition and proofs.


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