Stable and isoperimetric regions in some weighted manifolds with boundary Rosales Lombardo, Manuel César Weighted manifolds Riemannian cylinders Isoperimetric problems Stable sets 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 behavior of the Bakry–Émery– 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 Ω × 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 Ω × {t}. 2021-03-15T11:41:54Z 2021-03-15T11:41:54Z 2021-04 info:eu-repo/semantics/article Rosales, C. (2020). Stable and isoperimetric regions in some weighted manifolds with boundary. Nonlinear Analysis, 205, 112217. [https://doi.org/10.1016/j.na.2020.112217] http://hdl.handle.net/10481/67229 10.1016/j.na.2020.112217 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España Pergamon Elsevier Science LTD