Inserted: 24 mar 2020
Last Updated: 31 aug 2021
Journal: Ann. Fenn. Math.
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