# Sharp quantitative isoperimetric inequalities in the $L^1$ Minkowski plane - Mathematics > Functional Analysis

Sharp quantitative isoperimetric inequalities in the $L^1$ Minkowski plane - Mathematics > Functional Analysis - Download this document for free, or read online. Document in PDF available to download.

Abstract: We prove that a plane domain which is almost isoperimetric with respect tothe $L^1$ metric is close to a square whose sides are parallel to thecoordinates axis. Closeness is measured either by $L^\infty$ Haussdorf distanceor Fraenkel asymmetry. In the first case, we determine the extremal domains.

Author: Benoit Kloeckner IF

Source: https://arxiv.org/