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A non local approximation of the Gaussian perimeter: Gamma convergence and Isoperimetric properties

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    * Corresponding author 
The first author is partially supported by the NSF DMS Grant No. 1906451. The second author has been partially supported by the Academy of Finland grant 314227
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  • We study a non local approximation of the Gaussian perimeter, proving the Gamma convergence to the local one. Surprisingly, in contrast with the local setting, the halfspace turns out to be a volume constrained stationary point if and only if the boundary hyperplane passes through the origin. In particular, this implies that Ehrhard symmetrization can in general increase the non local Gaussian perimeter taken into consideration.

    Mathematics Subject Classification: Primary: 49Q15, 49Q20.

    Citation:

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