Calculus of Variations and Geometric Measure Theory

A. Mondino - S. Nardulli

Existence of isoperimetric regions in non-compact Riemannian manifolds under Ricci or scalar curvature conditions

created by mondino on 01 Oct 2012
modified by nardulli on 31 Jul 2019


Published Paper

Inserted: 1 oct 2012
Last Updated: 31 jul 2019

Journal: Communications in Analysis and Geometry
Pages: 17
Year: 2012


We prove existence of isoperimetric regions for every volume in non-compact Riemannian $n$-manifolds $(M,g)$, $n\geq 2$, having Ricci curvature $Ric_g \geq (n-1) k_0 g$ and being locally asymptotic to the simply connected space form of constant sectional curvature $k_0$; moreover in case $k_0=0$ we show that the isoperimetric regions are indecomposable. We also discuss some physically and geometrically relevant examples. Finally, under assumptions on the scalar curvature we prove existence of isoperimetric regions of small volume.

Tags: GeMeThNES