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- W4287705019 abstract "In a Riemannian manifold with a smooth positive function that weights the associated Hausdorff measures we study stable sets, i.e., second order minima of the weighted perimeter under variations preserving the weighted volume. By assuming local convexity of the boundary and certain behaviour of the Bakry-'Emery-Ricci tensor we deduce rigidity properties for stable sets by using deformations constructed from parallel vector fields tangent to the boundary. As a consequence, we completely classify the stable sets in some Riemannian cylinders $Omegatimesmathbb{R}$ with product weights. Finally, we also establish uniqueness results showing that any minimizer of the weighted perimeter for fixed weighted volume is bounded by a horizontal slice $Omegatimes{t}$." @default.
- W4287705019 created "2022-07-26" @default.
- W4287705019 creator A5008012446 @default.
- W4287705019 date "2020-07-26" @default.
- W4287705019 modified "2023-09-24" @default.
- W4287705019 title "Stable and isoperimetric regions in some weighted manifolds with boundary" @default.
- W4287705019 doi "https://doi.org/10.48550/arxiv.2007.13107" @default.
- W4287705019 hasPublicationYear "2020" @default.
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