Abstract

The regular N-gon provides the minimal Cheeger constant in the class of all N-gons with fixed volume. This result is due to a work of D. Bucur and I. Fragalà [A Faber-Krahn inequality for the Cheeger Constant of N-gons, J. of Geometric Analysis (2014)]. In this note, we address the stability of their result in terms of the L1 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

Author information

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Marco Caroccia

Dip. di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy

caroccia.marco@gmail.com

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Suggested citation

M. Caroccia, R. Neumayer. “A Note on the Stability of the Cheeger Constant of N-gons.” Journal of Convex Analysis 22 (2015), No. 4, 1207–1213. https://doi.org/10.68381/jca22063

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Published by Heldermann Verlag, 2015. Rights now held by Banach Press LLC.