Ricci flow and nonnegativity of sectional curvature

By Lei Ni. 2004

49 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/908b58a6ee8aeef770b4390511df1f1642a5c81e

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Pseudolocality for the Ricci Flow and Applications (2007, background): “Some estimates are also obtained for complete manifolds with nonnegative Ricci curvature by Ni [ 21 ].”
Some gradient estimates for the heat equation on domains and for an equation by Perelman (2006, background): “For related results on local lower and upper bounds for fundamental solutions of (3.2) and for a global lower bound for the conjugate of (3.2) in the spirit of Perelman, please see the interesting papers [G], [ Ni1 ] and [Ni2].”
Complete manifolds with nonnegative curvature operator (2006, methodology): “If evoking Theorem 2.3 of [ N1 ], the splitting result on solutions of Ricci flow on complete Riemannian manifold with nonnegative curvature operator, we can write a similar statement even when M is not assume to be compact.”
The conjugate heat equation and Ancient solutions of the Ricci flow (2010, methodology): “Previous related results along the Ricci flow setting can be found in [11, 23, 25, 29].”
Notes on Perelman's papers (2006, background): “We have uniform estimates on the functions {hk}k=1 and their spatial derivatives; compare [26, 45].”
Sharp logarithmic Sobolev inequalities on gradient solitons and applications (2008, unknown): “Then the result follows from the strong tensor maximum principle and a splitting theorem of noncompact manifolds proved in [28].”
A matrix Li-Yau-Hamilton estimate for Kähler-Ricci flow (2007, methodology): “In order to prove (5.6) one just need to apply the maximum principle (cf. [NT2, N5 ]) and notice that”
Gradient estimates for the heat equation under the Ricci flow (2009, methodology): “Ni’s work [24] offers yet another way to use the Ricci flow combined with the heat equation to study the evolution of g(x, t).”