For a complete noncompact Riemannian manifold with bounded geometry, we prove a “generalized” compactness result for sequences of finite perimeter sets with uniformly bounded volume and perimeter in a larger space obtained by adding limit manifolds at infinity. We extend previous results contained in Nardulli (Asian J Math 18(1):1–28, 2014), in such a way that the main theorem is a generalization of the generalized existence theorem, i.e., Theorem 1 of Nardulli (Asian J Math 18(1):1–28, 2014). We replace C^2,α locally asymptotic bounded geometry with C⁰ locally asymptotic bounded geometry.

中文翻译：

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有限周集的广义紧性及其在等渗问题中的应用

对于具有边界几何的完整非紧凑黎曼流形，我们证明了通过在无限大处添加极限流形而获得的具有更大空间的有限边界集序列的有限区域集的“广义”紧致性结果。我们以Nardulli（Asian J Math 18（1）：1-28，2014）中包含的先前结果为扩展，以使主要定理是广义存在定理的推广，即Nardulli（Asian J Math 18（1）：1-28，2014）。我们用C ⁰局部渐近有界几何替换C ^2，α局部渐近有界几何。