Isoperimetric inequalities in cylinders with density Castro, Katherine Existence of isoperimetric regions Manifolds with density Preserving isometries Cocompactly Cylinders with density The author has been supported by MICINN-FEDER, Spain grants MTM2010-21206-C02-01 , MTM2013-48371-C2-1-P , MEC-Feder grants MTM2017-84851-C2-1-P and PID2020-118180GB-I00 , and Junta de Andalucía, Spain grants A-FQM-441-UGR18 and P20-00164 . Open Access funding: Universidad de Granada/CBUA. Given a compact Riemannian manifold with density M without boundary and the real line R with constant density, we prove that isoperimetric regions of large volume in M×R with the product density are slabs of the form M×[a,b]. We previously prove, as a necessary step, the existence of isoperimetric regions in any manifold of density where a subgroup of the group of transformations preserving weighted perimeter and volume acts cocompactly. 2022-01-10T13:30:52Z 2022-01-10T13:30:52Z 2022-04 info:eu-repo/semantics/article K. Castro. Isoperimetric inequalities in cylinders with density. Nonlinear Analysis 217 (2022) 112726. [https://doi.org/10.1016/j.na.2021.112726] http://hdl.handle.net/10481/72281 10.1016/j.na.2021.112726 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España Elsevier