Geodesic
A Note on the Stability of the Cheeger Constant of N-gons
Journal of convex analysis, Tome 22 (2015) no. 4, pp. 1207-1214
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

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. 
@article{JCA_2015_22_4_JCA_2015_22_4_a15,
     author = {M. Caroccia and R. Neumayer},
     title = {A {Note} on the {Stability} of the {Cheeger} {Constant} of {N-gons}},
     journal = {Journal of convex analysis},
     pages = {1207--1214},
     year = {2015},
     volume = {22},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2015_22_4_JCA_2015_22_4_a15/}
}
TY  - JOUR
AU  - M. Caroccia
AU  - R. Neumayer
TI  - A Note on the Stability of the Cheeger Constant of N-gons
JO  - Journal of convex analysis
PY  - 2015
SP  - 1207
EP  - 1214
VL  - 22
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/JCA_2015_22_4_JCA_2015_22_4_a15/
ID  - JCA_2015_22_4_JCA_2015_22_4_a15
ER  - 
%0 Journal Article
%A M. Caroccia
%A R. Neumayer
%T A Note on the Stability of the Cheeger Constant of N-gons
%J Journal of convex analysis
%D 2015
%P 1207-1214
%V 22
%N 4
%U http://geodesic.mathdoc.fr/item/JCA_2015_22_4_JCA_2015_22_4_a15/
%F JCA_2015_22_4_JCA_2015_22_4_a15
M. Caroccia; R. Neumayer. A Note on the Stability of the Cheeger Constant of N-gons. Journal of convex analysis, Tome 22 (2015) no. 4, pp. 1207-1214. http://geodesic.mathdoc.fr/item/JCA_2015_22_4_JCA_2015_22_4_a15/