Strong uniqueness of the Ricci flow

DOI10.4310/jdg/1246888488zbMath1177.53036arXiv0706.3081OpenAlexW2963319380WikidataQ115171832 ScholiaQ115171832MaRDI QIDQ841577

Bing-Long Chen

Publication date: 18 September 2009

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.3081

zbMATH Keywords

complete noncompact caseRicci flow equation

Mathematics Subject Classification ID

Related Items (only showing first 100 items - show all)

Gradient Ricci solitons with vanishing conditions on Weyl ⋮ On the regular-convexity of Ricci shrinker limit spaces ⋮ Heat kernel on smooth metric measure spaces and applications ⋮ Eigenvalues of the drifting Laplacian on complete noncompact Riemannian manifolds ⋮ On four-dimensional steady gradient Ricci solitons that dimension reduce ⋮ Local curvature estimates for the Ricci-harmonic flow ⋮ Time analyticity for the heat equation on gradient shrinking Ricci solitons ⋮ On the relation between Ricci-harmonic solitons and Ricci solitons ⋮ On \(\kappa\)-noncollapsed complete noncompact shrinking gradient Ricci solitons which split at infinity ⋮ Volume growth for gradient shrinking solitons of Ricci-harmonic flow ⋮ Upper bounds on the first eigenvalue for a diffusion operator via Bakry-Émery Ricci curvature. II ⋮ Lagrangian self-similar solutions in gradient shrinking Kähler-Ricci solitons ⋮ Lower bounds for the scalar curvature of noncompact gradient solitons of List's flow ⋮ On the classification of four-dimensional gradient Ricci solitons ⋮ Local smoothing results for the Ricci flow in dimensions two and three ⋮ Some uniqueness results for Ricci solitons ⋮ Conformal invariants measuring the best constants for Gagliardo-Nirenberg-Sobolev inequalities ⋮ Conical structure for shrinking Ricci solitons ⋮ Kähler-Ricci shrinkers and ancient solutions with nonnegative orthogonal bisectional curvature ⋮ Rigidity of \(\kappa \)-noncollapsed steady Kähler-Ricci solitons ⋮ Rigid properties of quasi-almost-Einstein metrics ⋮ \(\epsilon\)-regularity for shrinking Ricci solitons and Ricci flows ⋮ Classification of gradient shrinking Ricci solitons with bounded Ricci curvature ⋮ The rigidity of \(\mathbb{S}^3 \times \mathbb{R}\) under ancient Ricci flow ⋮ Potential function estimates for quasi-Einstein metrics ⋮ On the potential function of gradient steady Ricci solitons ⋮ A note on existence of exhaustion functions and its applications ⋮ Ricci flows with unbounded curvature ⋮ The evolution of the Weyl tensor under the Ricci flow ⋮ Complete gradient shrinking Ricci solitons with pinched curvature ⋮ Liouville-type theorems on the complete gradient shrinking Ricci solitons ⋮ Remark on a diameter bound for complete Riemannian manifolds with positive Bakry-Émery Ricci curvature ⋮ How to produce a Ricci flow via Cheeger-Gromoll exhaustion ⋮ On gradient Ricci solitons ⋮ Ricci flow of warped Berger metrics on \(\mathbb{R}^4 \) ⋮ Rotational symmetry of self-similar solutions to the Ricci flow ⋮ \(C_0\)-positivity and a classification of closed three-dimensional CR torsion solitons ⋮ On Bach-flat gradient shrinking Ricci solitons ⋮ Ricci flow of homogeneous manifolds ⋮ On evolution equations under the Hamilton's Ricci flow ⋮ Ricci flow under local almost non-negative curvature conditions ⋮ The conjugate heat equation and ancient solutions of the Ricci flow ⋮ Higher dimensional steady Ricci solitons with linear curvature decay ⋮ Heat kernel on Ricci shrinkers ⋮ Omori-Yau maximum principles, \(V\)-harmonic maps and their geometric applications ⋮ Lower bounds for the scalar curvatures of noncompact gradient Ricci solitons ⋮ Schrödinger heat kernel upper bounds on gradient shrinking Ricci solitons ⋮ Classification of almost Yamabe solitons in Euclidean spaces ⋮ Four-dimensional complete gradient shrinking Ricci solitons ⋮ Perelman's entropy on ancient Ricci flows ⋮ Rigidity of complete generic shrinking Ricci solitons ⋮ Weakly PIC1 manifolds with maximal volume growth ⋮ Geometric properties of self-shrinkers in cylinder shrinking Ricci solitons ⋮ Ricci flow on asymptotically Euclidean manifolds ⋮ Ricci flow of regions with curvature bounded below in dimension three ⋮ Three circle theorems for eigenfunctions on complete shrinking gradient Ricci solitons with constant scalar curvature ⋮ Level set flow in 3D steady gradient Ricci solitons ⋮ Integral Ricci curvature bounds along geodesics for nonexpanding gradient Ricci solitons ⋮ On the asymptotic behavior of expanding gradient Ricci solitons ⋮ Conformal diffeomorphisms of gradient Ricci solitons and generalized quasi-Einstein manifolds ⋮ On the essential spectrum of complete non-compact manifolds ⋮ Maximum principles and gradient Ricci solitons ⋮ Generalization of the Hamilton-Ivey estimate to the higher dimensional Ricci flow with a vanishing Weyl tensor ⋮ On a classification of 4-d gradient Ricci solitons with harmonic Weyl curvature ⋮ On the asymptotic reduced volume of the Ricci flow ⋮ Generalized Ricci flow. II. Existence for complete noncompact manifolds ⋮ Remark on a lower diameter bound for compact shrinking Ricci solitons ⋮ Instantaneously complete Chern-Ricci flow and Kähler-Einstein metrics ⋮ Lower bound of the scalar curvature for quasi-Einstein metrics ⋮ Local mollification of Riemannian metrics using Ricci flow, and Ricci limit spaces ⋮ Classification of gradient Kähler-Ricci solitons with vanishing \(B\)-tensor ⋮ Liouville theorems, volume growth, and volume comparison for Ricci shrinkers ⋮ Positive solutions to Schrödinger equations and geometric applications ⋮ Sharp upper diameter bounds for compact shrinking Ricci solitons ⋮ Steady Ricci solitons with horizontally \(\epsilon\)-pinched Ricci curvature ⋮ Gradient shrinking Ricci solitons of half harmonic Weyl curvature ⋮ On gradient shrinking Ricci solitons with radial conditions ⋮ Kähler manifolds with almost nonnegative curvature ⋮ Classification of gradient steady Ricci solitons with linear curvature decay ⋮ Rigidity of complete gradient shrinkers with pointwise pinching Riemannian curvature ⋮ Curvature estimates for four-dimensional gradient steady Ricci solitons ⋮ Classification of gradient expanding and steady Ricci solitons ⋮ On gradient shrinking and expanding Kähler-Ricci solitons ⋮ New volume comparison results and applications to degeneration of Riemannian metrics ⋮ Volume growth estimates for Ricci solitons and quasi-Einstein manifolds ⋮ Producing 3D Ricci flows with nonnegative Ricci curvature via singular Ricci flows ⋮ Volume growth estimates of gradient Ricci solitons ⋮ Ends of gradient Ricci solitons ⋮ Chern-Ricci flows on noncompact complex manifolds ⋮ Curvature growth of some 4-dimensional gradient Ricci soliton singularity models ⋮ On the uniqueness of Ricci flow ⋮ Rigid properties for gradient generalized \(m\)-quasi-Einstein manifolds and gradient shrinking Ricci solitons ⋮ Eigenvalues of the drifting Laplacian on smooth metric measure spaces ⋮ Singularity models in the three-dimensional Ricci flow ⋮ Uniqueness of instantaneously complete Ricci flows ⋮ On four-dimensional anti-self-dual gradient Ricci solitons ⋮ Lower bounds for the scalar curvatures of Ricci flow singularity models ⋮ Small curvature concentration and Ricci flow smoothing ⋮ A note on Codazzi tensors ⋮ Rotational symmetry of conical Kähler-Ricci solitons

This page was built for publication: Strong uniqueness of the Ricci flow