Consider an open domain D on the plane, whose isoperimetric deficit is smaller than 1. This note shows that the difference between the barycenter of D and the barycenter of its boundary is bounded above by a constant times the isoperimetric deficit to the power 1/4. This power can be improved to 1/2, when D is furthermore assumed to be a convex domain, in any Euclidean space of dimension larger than 2. Keywords: Isoperimetric inequality on the plane, isoperimetric deficit, boundary barycenter, convex domains, isoperimetric stability.
Publié le : 2016-11-19
Classification:
Isoperimetric inequality on the plane,
isoperimetric deficit,
boundary barycenter,
convex domains,
isoperimetric stability.,
MSC2010: primary: 51M04, secondary: 51M25, 51M16, 52A20, 52A40, 41A25.,
[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA]
@article{hal-01399530,
author = {Miclo, Laurent},
title = {Isoperimetric stability of boundary barycenters in the plane},
journal = {HAL},
volume = {2016},
number = {0},
year = {2016},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01399530}
}
Miclo, Laurent. Isoperimetric stability of boundary barycenters in the plane. HAL, Tome 2016 (2016) no. 0, . http://gdmltest.u-ga.fr/item/hal-01399530/