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

@article{Mondino2012ExistenceOI,
  title={Existence of isoperimetric regions in non-compact Riemannian manifolds under Ricci or scalar curvature conditions},
  author={A. Mondino and S. Nardulli},
  journal={Communications in Analysis and Geometry},
  year={2012},
  volume={24},
  pages={115-138}
}
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… Expand
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