Lectures on the Ricci Flow

By P. Topping. 2006

335 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/bac62b39ea2305306163659c3775106905a853c1

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Citations in the corpus

Sharp logarithmic Sobolev inequalities on gradient solitons and applications (2008, result): “For expanding solitons, we also obtain a volume estimate, which generalizes a recent result of Hamilton [22], see also [11], asserting that the asymptotic volume ratio of gradient expanding solitons with bounded positive Ricci curvature must be positive.”
Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics (2010, background): “(See [17] for a discussion of these issues.”
Rotational symmetry of self-similar solutions to the Ricci flow (2012, methodology): “ve LW(g) satisﬁes ∆L(LW(g)) +LX(LW(g)) = 0. SELF-SIMILAR SOLUTIONS TO THE RICCI FLOW 15 Proof. Let g(s) be a smooth one-parameter family of metrics with g(0) = g. It follows from Proposition 2.3.7 in [26] that (14) ∂ ∂s Ricg(s) s=0 = − 1 2 ∆Lh+ 1 2 LZ(g), where h= ∂ ∂sg(s) s=0 and Z= divh− 1 2 ∇(trh”
Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds (2008, unknown): “3 on page 10 of [11]).”
Ricci flow coupled with harmonic map flow (2009, background): “Introductory surveys on the Ricci flow and Perelman’s functionals can be found in the books by Chow and Knopf [4], Chow, Lu and Ni [7], Müller [27] and Topping [43].”
Notes on Perelman's papers (2006, background): “Along with these people we thank Mike Anderson, Albert Chau, Ben Chow, Xianzhe Dai, Jonathan Dinkelbach, Sylvain Maillot, John Morgan, Joan Porti, Gang Tian, Peter Topping, Bing Wang, Guofang Wei, Hartmut Weiss, Burkhard Wilking, Jon Wolfson, Rugang Ye and Maciej Zworski.”
Gradient estimates for the heat equation under the Ricci flow (2009, background): “To learn about the history, the intuitive meaning, the technical aspects, and the applications of the Ricci flow, one should refer to the many quality books on the subject such as, for example, [12, 33, 23, 9, 10].”
Poincaré and Brunn-Minkowski inequalities on the boundary of weighted Riemannian manifolds (2017, background): “[75]), we propose to add another tangential component τt to (6.”
The Existence of Type II Singularities for the Ricci Flow on $S^{n+1}$ (2007, background): “We remark that some beautiful intuitions of the forming of Type II singularity were described and explained by Chow-Knopf in [14] and Topping in [32].”
Numerical methods for finding stationary gravitational solutions (2015, background): “[82] P.”