| 董莲莲,王培合,温玉亮.偶数维Riemannian流形的直径估计[J].数学年刊A辑,2009,30(6):787~792 |
| 偶数维Riemannian流形的直径估计 |
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| Received:December 31, 2008 |
| DOI： |
| 中文关键词: 直径, 体积比较定理, Hausdorff收敛 |
| 英文关键词:Diameter, Volume comparison theorem, Hausdorff convergence |
| 基金项目: |
| Author Name | Affiliation | E-mail | | DONG Lianlian | School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China. | lianlian198282@163.com | | WANG Peihe | School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China. | peihewang@hotmail.com | | WEN Yuliang | Department of Mathematics, East China Normal University, Shanghai 200062, China. | ylwen@math.ecnu.edu.cn |
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| 中文摘要: |
| 设M2n是2n维紧致无边单连通的Riemannian流形, S2n为欧氏空间R2n+1中的单位球面. 探讨了满足截面曲率KM∈(0,1], 体积 0< V(M)≤2(1+η)V(B?π) 的流形M2n的直径估计,这里η是某个仅依赖于n的正数, B?π是S2n上半径为?π的测地球,并且给出了这类流形上的一个gap现象及流形上Laplacian算子第一特征值的一个下界估计. |
| 英文摘要: |
| Let M2n be a 2n-dimensional compact, simply connected Riemannian manifold without boundary and S2n be the unit sphere in Euclidean space R2n+1. The authors derive an estimate of the diameter in this note whenever the manifold concerned satisfies that the sectional curvature KM varies in (0,1] and the volume V(M) is not larger than 2(1+η)V(B?π) for some positive number η depending only on n, where B?π is the geodesic ball on S2n with radius ?π. A gap phenomenon of the manifold concerned is given and finally a lower bound of the first eigenvalue of Laplacian operator on manifold M is obtained. |
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