The $\epsilon -{\epsilon }^{\beta }$ property in the isoperimetric problem with double density, and the regularity of isoperimetric sets

Abstract

We prove the validity of the $\epsilon -{\epsilon }^{\beta }$ property in the isoperimetric problem with double density, generalising the known properties for the case of single density. As a consequence, we derive regularity for isoperimetric sets.

arXiv comment19 pages, 1 figure

References in corpus (6)

• Regularity of sets with quasiminimal boundary surfaces in metric spaces
• On the isoperimetric problem with double density
• Weighted Cheeger sets are domains of isoperimetry
• Isoperimetric problem in H-type groups and Grushin spaces
• Isoperimetric Regions in ${\mathbb{R}}^n$ with density $r^p$
• Symmetric double bubbles in the Grushin plane

Cited by in corpus (5)

• Isoperimetric sets in spaces with lower bounds on the Ricci curvature
• Topological regularity of isoperimetric sets in PI spaces having a deformation property
• On the Steiner property for planar minimizing clusters. The anisotropic case
• On the Steiner property for planar minimizing clusters. The isotropic case
• On the monotonicity of weighted perimeters of convex bodies