@misc{10481/67229,
year = {2021},
month = {4},
url = {http://hdl.handle.net/10481/67229},
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 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}.},
organization = {MINECO, Spain 

MTM2017-84851-C2-1-P},
organization = {Junta de Andalucía

European Commission

FQM325},
publisher = {Pergamon Elsevier Science LTD},
keywords = {Weighted manifolds},
keywords = {Riemannian cylinders},
keywords = {Isoperimetric problems},
keywords = {Stable sets},
title = {Stable and isoperimetric regions in some weighted manifolds with boundary},
doi = {10.1016/j.na.2020.112217},
author = {Rosales Lombardo, Manuel César},
}