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| In this talk we describe global minimizers and second order minima of the weighted perimeter for fixed weighted volume inside an open half-space or slab $\Omega$ in $\mathbb{R}^{n+1}$ endowed with a perturbation of the Gaussian density of the form $f(p):=\exp(\omega(p)-c|p|^2)$, where $c>0$ and $\omega$ is a concave function only depending on the signed distance from the linear hyperplane parallel to $\partial\Omega$. |
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