We show existence and we give a geometric characterization of isoperimetric regions for large volumes, in $C^2$-locally asymptotically Euclidean Riemannian manifolds with a finite number of $C^0$-asymptotically Schwarzschild ends. This work extends previous results contained in [EM13b], [EM13a], and [BE13]. Moreover strengthening a little bit the speed of convergence to the Schwarzschild metric we obtain existence of isoperimetric regions for all volumes for a class of manifolds that we named $C^0$-strongly asymptotic Schwarzschild, extending results of [BE13]. Such results are of interest in the field of mathematical general relativity.

中文翻译：

---

有限个$ C ^ 0 $渐近Schwarzschild末端的完整黎曼流形的等渗问题

我们展示了存在性，并给出了等体积区域的几何特征，在$ C ^ 2 $-局部渐近欧几里德黎曼流形中，有限数量的$ C ^ 0 $-渐近Schwarzschild端。这项工作扩展了[EM13b]，[EM13a]和[BE13]中包含的先前结果。此外，稍微提高了收敛到Schwarzschild度量的收敛速度，我们获得了我们将$ C ^ 0 $-强渐近Schwarzschild的一类流形的所有体积的等压区域的存在，从而扩展了[BE13]的结果。这样的结果在数学广义相对论领域中是令人感兴趣的。