Isoperimetric inequalities in cylinders with density. (April 2022)

• Record Type: Journal Article
• Authors: Castro, Katherine
• Is Part Of: Nonlinear analysis. Volume 217(2022)
• Publication Date: 2022-04
• Subjects: Existence of isoperimetric regions -- Manifolds with density -- Preserving isometries -- Cocompactly -- Cylinders with density; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112726
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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.