Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities - Fusco, Nicola; Maggi, Francesco; Pratelli, Aldo (Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 2009)
The first eigenvalue of the p-Laplacian on an open set of given measure attains its minimum value if and only if the set is a ball. We provide a quantitative version of this statement by an argument that can be easily adapted to treat also certain isocapacitary and Cheeger inequalities.