Isoperimetric problem for exponential measure on the plane with l_1-metric

Abstract

We give a solution to the isoperimetric problem for the exponential measure on the plane with the ${\ell }_1$-metric. As it turns out, among all sets of a given measure, the simplex or its complement (i.e. the ball in the ${\ell }_1$-metric or its complement) has the smallest boundary measure. The proof is based on a symmetrisation (along the sections of equal ${\ell }_1$-distance from the origin).

arXiv comment12 pages, 6 figures

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