A compactness theorem for complete Ricci shrinkers

DOI10.1007/s00039-011-0137-4zbMath1239.53056arXiv1005.3255OpenAlexW1972411226MaRDI QIDQ659926

Robert Haslhofer, Reto Muller

Publication date: 24 January 2012

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.3255

zbMATH Keywords

Hamilton's Ricci flowconvergence in the pointed Cheeger-Gromov sensegradient shrinkers

Mathematics Subject Classification ID

Related Items (41)

On the regular-convexity of Ricci shrinker limit spaces ⋮ A necessary and sufficient condition for Ricci shrinkers to have positive AVR ⋮ Convergence of Ricci flows with bounded scalar curvature ⋮ Time analyticity for the heat equation on gradient shrinking Ricci solitons ⋮ On \(\kappa\)-noncollapsed complete noncompact shrinking gradient Ricci solitons which split at infinity ⋮ On the structure of Ricci shrinkers ⋮ On the equivalence between noncollapsing and bounded entropy for ancient solutions to the Ricci flow ⋮ A note on the compactness theorem for 4d Ricci shrinkers ⋮ \(\epsilon\)-regularity for shrinking Ricci solitons and Ricci flows ⋮ Sharp Gaussian upper bounds for Schrödinger heat kernel on gradient shrinking Ricci solitons ⋮ A gap theorem on complete shrinking gradient Ricci solitons ⋮ Rigidity of complex projective spaces in Ricci shrinkers ⋮ Harmonic and Schrödinger functions of polynomial growth on gradient shrinking Ricci solitons ⋮ Compactness theory of the space of super Ricci flows ⋮ Shrinkers with curvature-pinching conditions are compact ⋮ Liouville-type theorems on the complete gradient shrinking Ricci solitons ⋮ A uniqueness theorem for asymptotically cylindrical shrinking Ricci solitons ⋮ The entropy of Ricci flows with Type-I scalar curvature bounds ⋮ Bubble-tree convergence and local diffeomorphism finiteness for gradient Ricci shrinkers ⋮ Regularity and compactness of harmonic-Einstein equations ⋮ Heat kernel on Ricci shrinkers ⋮ Lower bounds for the scalar curvatures of noncompact gradient Ricci solitons ⋮ Geometry of manifolds with densities ⋮ The stability inequality for Ricci-flat cones ⋮ Schrödinger heat kernel upper bounds on gradient shrinking Ricci solitons ⋮ The rigidity of Ricci shrinkers of dimension four ⋮ The size of the singular set of a type I Ricci flow ⋮ The energy of a smooth metric measure space and applications ⋮ Geometry of shrinking Ricci solitons ⋮ Liouville theorems, volume growth, and volume comparison for Ricci shrinkers ⋮ Positive solutions to Schrödinger equations and geometric applications ⋮ A bound for the order of the fundamental group of a complete noncompact Ricci shrinker ⋮ Sharp upper diameter bounds for compact shrinking Ricci solitons ⋮ A rigidity theorem for codimension one shrinking gradient Ricci solitons in \(\mathbb R^{n+1}\) ⋮ Gradient Kähler-Ricci solitons with nonnegative orthogonal bisectional curvature ⋮ Volume growth estimates for Ricci solitons and quasi-Einstein manifolds ⋮ Volume growth estimates of gradient Ricci solitons ⋮ Ends of gradient Ricci solitons ⋮ Curvature growth of some 4-dimensional gradient Ricci soliton singularity models ⋮ Regularity theory for type I Ricci flows ⋮ Small curvature concentration and Ricci flow smoothing

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