论文标题
Uryson宽度，渐近维度和RICCI曲率
Uryson Width, Asymptotic Dimension and Ricci Curvature
论文作者
论文摘要
如果存在从m到k维的多面体空间p的连续映射f，则riemannian n-manifold M具有k维的uryson宽度，该宽度的连续映射f，使所有点的回调f^{ - 1}（p）的所有点P中的所有点P）在P中具有c的直径为c。我们证明，n维riemannian歧管M具有至少n-k特征值的ricci曲率曲率，下面由正常数（n-1）b界定下，具有k维的Uryson宽度，该宽度由常数c> 0界定。常数C仅取决于b。 特别是，因此，其riemannian n-manifold m具有标态曲率s的下面由正常常数n（n-1）s构成的riemannian n-manifold m具有（n-1）二维的uryson宽度，该宽度仅取决于c> 0。该结果证实了Gromov M. Gromov的猜想。
A Riemannian n-manifold M has k-dimensional Uryson width bounded by a constant c >0 if there exists a continuous map f from M to an k-dimensional polyhedral space P, such that the pullbacks f^{-1}(p) of all points p in P have diameters bounded by c. We prove that an n-dimensional Riemannian manifold M with at least n-k eigenvalues of the Ricci curvature bounded below by a positive constant (n-1)b has k-dimensional Uryson width bounded by a constant c >0. The constant c depends only on b. In particular, it follows that a Riemannian n-manifold M with scalar curvature S bounded below by a positive constant n (n-1) s has (n-1)-dimensional Uryson width bounded by a constant c >0 depending only on s. This result confirms a conjecture of M. Gromov.
