Existence of isoperimetric regions in ${\mathbb{R}}^n$ with density

Abstract

We prove the existence of isoperimetric regions in ${\mathbb{R}}^n$ with density under various hypotheses on the growth of the density. Along the way we prove results on the boundedness of isoperimetric regions.

arXiv comment31 pages, 4 figures

Cited by in corpus (3)

• On the isoperimetric problem with double density
• On the Steiner property for planar minimizing clusters. The anisotropic case
• Isoperimetry in Surfaces of Revolution with Density