3-Manifolds with nonnegative Ricci curvature

Gang Liu

doi:10.1007/s00222-012-0428-x

3-Manifolds with nonnegative Ricci curvature

Gang Liu^*

^*Corresponding author for this work

University of Minnesota Twin Cities

Research output: Contribution to journal › Article › peer-review

51 Scopus citations

Abstract

For a complete noncompact 3-manifold with nonnegative Ricci curvature, we prove that either it is diffeomorphic to ℝ³ or the universal cover splits. This confirms Milnor's conjecture in dimension 3.

Original language	English
Pages (from-to)	367-375
Number of pages	9
Journal	Inventiones Mathematicae
Volume	193
Issue number	2
DOIs	https://doi.org/10.1007/s00222-012-0428-x
State	Published - Aug 2013
Externally published	Yes

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title = "3-Manifolds with nonnegative Ricci curvature",

abstract = "For a complete noncompact 3-manifold with nonnegative Ricci curvature, we prove that either it is diffeomorphic to ℝ3 or the universal cover splits. This confirms Milnor's conjecture in dimension 3.",

author = "Gang Liu",

year = "2013",

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doi = "10.1007/s00222-012-0428-x",

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AB - For a complete noncompact 3-manifold with nonnegative Ricci curvature, we prove that either it is diffeomorphic to ℝ3 or the universal cover splits. This confirms Milnor's conjecture in dimension 3.

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DO - 10.1007/s00222-012-0428-x

M3 - 文章

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SN - 0020-9910

VL - 193

SP - 367

EP - 375

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

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ER -

3-Manifolds with nonnegative Ricci curvature

Abstract

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