1. Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants
- Author
-
Vesa Julin and Giorgio Maria Saracco
- Subjects
Gaussian ,media_common.quotation_subject ,01 natural sciences ,Upper and lower bounds ,Asymmetry ,Omega ,Combinatorics ,Set (abstract data type) ,Cheeger sets ,Cheeger constant ,quantitative inequalities ,symbols.namesake ,Mathematics - Analysis of PDEs ,Euclidean geometry ,FOS: Mathematics ,Mathematics::Metric Geometry ,0101 mathematics ,epäyhtälöt ,Mathematics ,media_common ,49Q10, 49Q20, 39B62 ,osittaisdifferentiaaliyhtälöt ,010102 general mathematics ,Articles ,Cheeger constant (graph theory) ,010101 applied mathematics ,symbols ,Analysis of PDEs (math.AP) - Abstract
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., Comment: 18 pages, 3 figures
- Published
- 2021