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| THE VOLUME AND TOPOLOGY OF A COMPLETE REIMANNIAN MANIFOLD |
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Citation： |
ZHAN Huashui,SHEN Zhongmin.THE VOLUME AND TOPOLOGY OF A COMPLETE REIMANNIAN MANIFOLD[J].Chinese Annals of Mathematics B,2001,22(1):85~92 |
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Net amount： 856 |
Authors： |
ZHAN Huashui; SHEN Zhongmin |
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| Abstract： |
It is conjectured that the manifold with nonnegative Ricci curvature and weaked bounded geometry is of finite topological type, if
$$\lim_{r \rightarrow \infty} \frac{vol[B(p,r)]}{r^2} = 0$$.
The paper partially solves this conjecture. In the same time, the paper also discusses the volume growth of a manifold with asymptotically nonnegative Ricci curvature. |
Keywords： |
Ricci curvature, Weak bounded geometry, Finite topological type, Volume growth |
Classification： |
53C20 |
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