A Note on the Stability of the Cheeger Constant of N-gons
Copyright policy )A Note on the Stability of the Cheeger Constant of N-gons
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 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
- NORTHEASTERN UNIVERSITY United States
- University of Pisa Italy
- University of Florence Italy
- The University of Texas at Austin United States
- University of Texas at Austin United States
Optimization of shapes other than minimal surfaces, Analysis of PDEs, FOS: Mathematics, Cheeger constant, stability, \(N\)-gons, Analysis of PDEs (math.AP)
Optimization of shapes other than minimal surfaces, Analysis of PDEs, FOS: Mathematics, Cheeger constant, stability, \(N\)-gons, Analysis of PDEs (math.AP)
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