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arXiv · 1606.03342

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

Marta Strzelecka
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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).

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Marta Strzelecka. 2016-06-10. Isoperimetric problem for exponential measure on the plane with l_1-metric. https://doi.org/10.1007/s11117-017-0476-y

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