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-  2018 

具有渐近非负Ricci曲率完备非紧的黎曼流形
Complete noncompact Riemannian manifold with asymptotically nonnegative Ricci curvature

DOI: 10.6040/j.issn.1671-9352.0.2017.480

Keywords: 渐近非负Ricci曲率,Excess函数,大体积增长,有限拓扑型,Busemann函数,
asymptotically nonnegative Ricci curvature
,Busemann function,finite topological type,Excess function,large volume growth

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Abstract:

摘要: 研究了一类具有渐近非负Ricci曲率完备非紧的n维黎曼流形,利用推广的Excess函数和Busemann函数,证明了具有渐近非负Ricci曲率完备非紧的n维黎曼流形在kp(r)≥-C/((1+r)α)和大体积增长的条件下具有有限拓扑型,从而推广了已有的一系列结果。
Abstract: We study the topology of complete noncompact Riemannian manifolds with asymptotically nonnegative Ricci curvature. By using extensions of Excess function and Busemann function, it is proved that they have finite topological type under sectional curvature bounded from nonnegative below kp(r)≥- C/((1+r)α) and large volume growth, which extend a series known results

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