
Journal of Convex Analysis 22 (2015), No. 4, 12071214 Copyright Heldermann Verlag 2015 A Note on the Stability of the Cheeger Constant of Ngons Marco Caroccia Dip. di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy caroccia.marco@gmail.com Robin Neumayer Dept. of Mathematics, University of Texas, Austin, TX 787120257, U.S.A. rneumayer@math.utexas.edu The regular Ngon provides the minimal Cheeger constant in the class of all Ngons with fixed volume. This result is due to a work of D. Bucur and I. Fragalà [A FaberKrahn inequality for the Cheeger Constant of Ngons, J. of Geometric Analysis (2014)]. In this note, we address the stability of their result in terms of the L^{1} distance between sets. Furthermore, we provide a stability inequality in terms of the Hausdorff distance between the boundaries of sets in the class of polygons having uniformly bounded diameter. Finally, we show that our results are sharp, both in the exponent of decay and in the notion of distance between sets. [ Fulltextpdf (107 KB)] for subscribers only. 