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- W2069897922 abstract "Abstract Let be an open half-space or slab in ℝ n+1 endowed with a perturbation of the Gaussian measureof the form f (p) := exp(ω(p) − c|p| 2 ), where c > 0 and ω is a smooth concave function depending only onthe signed distance from the linear hyperplane parallel to ∂ Ω. In this work we follow a variational approach to show that half-spaces perpendicular to ∂ Ω uniquely minimize the weighted perimeter in Ω among sets enclosing the same weighted volume. The main ingredient of the proof is the characterization of half-spacesparallel or perpendicular to ∂ Ω as the unique stable sets with small singular set and null weighted capacity.Our methods also apply for = ℝ n+1 , which produces in particular the classification of stable sets in Gaussspace and a new proof of the Gaussian isoperimetric inequality. Finally, we use optimal transport to studythe weighted minimizers when the perturbation term ω is concave and possibly non-smooth." @default.
- W2069897922 created "2016-06-24" @default.
- W2069897922 creator A5008012446 @default.
- W2069897922 date "2014-01-01" @default.
- W2069897922 modified "2023-09-27" @default.
- W2069897922 title "Isoperimetric and Stable Sets for Log-ConcavePerturbations of Gaussian Measures" @default.
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- W2069897922 doi "https://doi.org/10.2478/agms-2014-0014" @default.
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