Isoperimetric inequalities in cylinders with density

2021/08/06 by Castro, Katherine · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2108.03207

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.

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