Geodesic
Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants
Vesa Julin1 ; Giorgio Saracco2
1University of Jyväskylä, Department of Mathematics and Statistics
2Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 1071-1087
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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

Vesa Julin  1   ; Giorgio Saracco  2

1 University of Jyväskylä, Department of Mathematics and Statistics
2 Scuola Internazionale Superiore di Studi Avanzati (SISSA) 
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     title = {Quantitative lower bounds to the {Euclidean} and the {Gaussian} {Cheeger} constants},
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Vesa Julin; Giorgio Saracco. Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants. Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 1071-1087. http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a26/