Diameter estimate of the manifolds with positive Ricci curvature and reverse volume pinching

作者：Wang, Peihe^*; Jia, Shujuan

来源：Differential Geometry and its Applications, 2014, 32: 28-34.

DOI：10.1016/j.difgeo.2013.11.002

• k-th Ricci curvature
• Hausdorff convergence
• Diameter

We show that for any integer n >= 3, there exists a positive number eta(n) depending only on n such that if M-n is a complete simply connected n-dimensional Riemannian manifold whose sectional curvature, Ricci curvature and volume satisfy the conditions K-M <= 1, Ric(M) >= (n + 2)/4 and 0 < V(M) < 2(1 + eta) V (B-3/4 pi), respectively, then the diameter of M-n is less than 3 pi/2.

• 出版日期2014-2
• 单位曲阜师范大学