论文标题
在整体曲率边界和$ \ varepsilon $ range下，加权歧管直径的定量估计值
Quantitative estimate of diameter for weighted manifolds under integral curvature bounds and $\varepsilon$-range
论文作者
论文摘要
在本文中，我们将Sprouse和Hwang-Lee证明的紧凑性定理扩展到了加权歧管，假设加权RICCI曲率以其重量函数为界。借助$ \ varepsilon $ range，我们认为有效维度最多是$ 1 $，此外，有效维度至少是歧管的维度。为了显示这些定理，我们将cheger-Colding的段不平等扩展到加权歧管。
In this article, we extend the compactness theorems proved by Sprouse and Hwang-Lee to a weighted manifold under the assumption that the weighted Ricci curvature is bounded below in terms of its weight function. With the help of the $\varepsilon$-range, we treat the case that the effective dimension is at most $1$ in addition to the case that the effective dimension is at least the dimension of the manifold. To show these theorems, we extend the segment inequality of Cheeger-Colding to a weighted manifold.
