%0 Journal Article
%T Sharp quantitative isoperimetric inequalities in the $L^1$ Minkowski plane
%A Benoit Kloeckner
%J Mathematics
%D 2009
%I arXiv
%R 10.1090/S0002-9939-10-10366-9
%X We prove that a plane domain which is almost isoperimetric (with respect to the $L^1$ metric) is close to a square whose sides are parallel to the coordinates axis. Closeness is measured either by $L^\infty$ Haussdorf distance or Fraenkel asymmetry. In the first case, we determine the extremal domains.
%U http://arxiv.org/abs/0907.4945v1