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

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.

• Publication year

  2012

• Venue

  arXiv: Differential Geometry

• Publication date

  2012-10-01

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.4310/CAG.2016.v24.n1.a5arXiv 1210.0567
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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