We prove existence of isoperimetric regions for every volume in non-compactRiemannian $n$-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 ofconstant sectional curvature $k_0$; moreover in case $k_0=0$ we show that theisoperimetric regions are indecomposable. We also discuss some physically andgeometrically relevant examples. Finally, under assumptions on the scalarcurvature we prove existence of isoperimetric regions of small volume.
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机译：我们证明了非紧黎曼$ n $-流形$（M，g）$，$ n \ geq 2 $，具有Ricci曲率$ Ric_g \ geq（n-1）k_0 g $并且存在恒定截面曲率$ k_0 $的简单连通空间形式的局部渐近性;此外，在$ k_0 = 0 $的情况下，我们证明等距区域是不可分解的。我们还将讨论一些与物理和几何相关的示例。最后，在标量曲率的假设下，我们证明了等体积小区域的存在。
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