cvgmt: Existence of isoperimetric regions in $\R^n$ with density

Calculus of Variations and Geometric Measure Theory

F. Morgan - A. Pratelli

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

created by pratelli on 21 Oct 2025

[BibTeX]

preprint

Inserted: 21 oct 2025

Year: 2011

Abstract:

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