论文标题
标量曲率和熵下边界和体积上限下的Epsilon规律性
Epsilon regularity under scalar curvature and entropy lower bounds and volume upper bounds
论文作者
论文摘要
示例表明，在标态曲率上几乎具有欧几里得下限的Riemannian歧管，而Perelman熵在任何度量空间意义上都不必接近欧几里得空间。在这里，我们表明，如果一个人还假设几乎是欧几里得的上部绑在大量的大地球上，那么在这样一个空间中的单位球是Gromov-Hausdorff关闭的，实际上是Bi-Hölder和Bi-$ w^{1，P} $同型，同型同型，到Euclidean Balls。我们证明在相同的假设下是紧凑的，并限制了空间结构定理。
Examples show that Riemannian manifolds with almost-Euclidean lower bounds on scalar curvature and Perelman entropy need not be close to Euclidean space in any metric space sense. Here we show that if one additionally assumes an almost-Euclidean upper bound on volumes of geodesic balls, then unit balls in such a space are Gromov-Hausdorff close, and in fact bi-Hölder and bi-$W^{1,p}$ homeomorphic, to Euclidean balls. We prove a compactness and limit space structure theorem under the same assumptions.
