Wednesday, October 3, 2012

1210.0567 (Andrea Mondino et al.)

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

Andrea Mondino, Stefano Nardulli
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.
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