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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/



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