Complete Riemannian manifolds with pointwise pinched curvature

By Binglong Chen, Xiping Zhu. 2000

92 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2d1e2b7a2987e77bd71044631ce134304acf5a46

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In Applied Mathematics

1. Huaihuo Cao
2. Binglong Chen
3. Xiping Zhu
4. Lei Ni
5. Xiaohua Zhu
6. B.-l. Chen
7. Baoqiang Wu
8. F. Schulze

In Geometry and Topology

1. Huaihuo Cao
2. Binglong Chen
3. Xiping Zhu
4. Lei Ni
5. Xiaohua Zhu
6. B.-l. Chen
7. Baoqiang Wu
8. F. Schulze

Citations in the corpus

• A Uniformization Theorem Of Complete Noncompact K\"{a}hler Surfaces With Positive Bisectional Curvature (2002, background): “More importantly, by a blow up and blow down argument as in [6], we can prove that the curvature of the evolving metric decays linearly in time.”
• A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton-Perelman theory of the Ricci flow (2006, methodology): “(Characterization for nonnegatively curved Type III models was obtained in [30].”
• Recent developments on the Hamilton’s Ricci Flow (2007, background): “(ii) (Chen-Zhu [21]) Any Type III singularity model with nonnegative curvature operator and positive Ricci curvature must be a homothetically expanding Ricci soliton.”
• Recent Progress on Ricci Solitons (2009, background): “(Chen-Zhu [25]) Any Type III singularity model of the Ricci flow with nonnegative curvature operator and positive Ricci curvature must be a homothetically expanding Ricci soliton.”
• Hamilton-Perelman's Proof of the Poincar\'e Conjecture and the Geometrization Conjecture (2006, methodology): “Finally, in [31], Chen and the second author also used the Ricci flow to obtain the following flatness theorem for noncompact three-manifolds.”
• Complete manifolds with nonnegative curvature operator (2006, methodology): “Since for all g(t), its Ricci curvature satisfies (3.4), this holds up on the blowdown/blow-up solutions, which after passing to its universal cover, are either a nonflat gradient steady soliton or a nonflat gradient expanding soliton, with nonnegative curvature operator, by results from [H3] (Theor”
• Expanding solitons with non-negative curvature operator coming out of cones (2010, background): “9 of [25], where a similar result to that of [10] is proved using the W+ functional.”