论文标题
在簇和带有有限几何形状的Riemannian歧管中的多相位轮廓上
On clusters and the multi-isoperimetric profile in Riemannian manifolds with bounded geometry
论文作者
论文摘要
对于具有有界几何形状的完整的Riemannian歧管，我们证明了等等簇的存在，以及通过在Infinity上添加有限的许多极限歧管获得的较大空间中群集序列的紧凑定理。此外，我们表明等等簇是有界的。我们介绍并证明了多相位概况的持有人连续性，伊曼纽尔·米尔曼（Emanuel Milman）和乔·尼曼（Joe Neeman）探索了高斯的外围概念。我们提供了经典存在定理的证明，例如在空间形式中，使用此处介绍的结果。这项工作的结果概括了Stefano Nardulli，Andrea Mondino，Frank Morgan，Matteo Galli和ManuelRitoré，来自经典的Riemannian和Sub-Riemannian等等方面的问题，以及Riemannian Isoperimetric Crusters的背景以及Frank Morgan和Francesco Maggi的背景。
For a complete Riemannian manifold with bounded geometry, we prove the existence of isoperimetric clusters and also the compactness theorem for sequence of clusters in a larger space obtained by adding finitely many limit manifolds at infinity. Moreover, we show that isoperimetric clusters are bounded. We introduce and prove the Holder continuity of the multi-isoperimetric profile which has been explored by Emanuel Milman and Joe Neeman with a Gaussian-weighted notion of perimeter. We yield a proof of classical existence theorem, e.g. in space forms, for isoperimetric cluster using the results presented here. The results in this work generalize previous works of Stefano Nardulli, Andrea Mondino, Frank Morgan, Matteo Galli and Manuel Ritoré from the classical Riemannian and sub-Riemannian isoperimetric problem to the context of Riemannian isoperimetric clusters and also Frank Morgan and Francesco Maggi works on the clusters theory in the Euclidean setting.
