论文标题
正标曲率符合RICCI极限空间
Positive Scalar Curvature Meets Ricci Limit Spaces
论文作者
论文摘要
我们研究了均匀的正量表曲率对来自$ n $ manifolds的序列的非汇合RICCI极限空间的大小的影响，该序列具有非负RICCI曲率和均匀的正标曲率的序列。我们证明，这样的限制空间最多可以在$ n-2 $行或$ \ mathbb {r} $ - 因素上拆分。当发生这种最大分裂时，我们在非分离因子的直径上获得了一个均匀的上限。此外，我们获得了该歧管上测量球的体积差距估计值和体积增长顺序估计。
We investigate the influence of uniformly positive scalar curvature on the size of a non-collapsed Ricci limit space coming from a sequence of $n$-manifolds with non-negative Ricci curvature and uniformly positive scalar curvature. We prove that such a limit space splits at most $n-2$ lines or $\mathbb{R}$-factors. When this maximal splitting occurs, we obtain a uniform upper bound on the diameter of the non-splitting factor. Moreover, we obtain a volume gap estimate and a volume growth order estimate of geodesic balls on such manifolds.
