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arXiv · 2106.05641

Asymptotics of the $s$-fractional Gaussian perimeter as $s\to 0^+$

Alessandro Carbotti·Simone Cito·Domenico Angelo La Manna·Diego Pallara
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Abstract

We study the asymptotic behaviour of the renormalised $s$-fractional Gaussian perimeter of a set $E$ inside a domain $\Omega$ as $s\to 0^+$. Contrary to the Euclidean case, as the Gaussian measure is finite, the shape of the set at infinity does not matter, but, surprisingly, the limit set function is never additive.

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Alessandro Carbotti, Simone Cito, Domenico Angelo La Manna, Diego Pallara. 2021-06-10. Asymptotics of the $s$-fractional Gaussian perimeter as $s\to 0^+$. https://arxiv.org/abs/2106.05641

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