Sharp quantitative isoperimetric inequalities in the $L^1$ Minkowski plane
Functional Analysis
2013-02-08 v1 Differential Geometry
Abstract
We prove that a plane domain which is almost isoperimetric (with respect to the metric) is close to a square whose sides are parallel to the coordinates axis. Closeness is measured either by Haussdorf distance or Fraenkel asymmetry. In the first case, we determine the extremal domains.
Cite
@article{arxiv.0907.4945,
title = {Sharp quantitative isoperimetric inequalities in the $L^1$ Minkowski plane},
author = {Benoit Kloeckner},
journal= {arXiv preprint arXiv:0907.4945},
year = {2013}
}
Comments
9 pages