Space of Ricci flows (II)

Abstract

Based on the compactness of the moduli of non-collapsed Calabi-Yau spaces with mild singularities, we set up a structure theory for polarized Kähler Ricci flows with proper geometric bounds. Our theory is a generalization of the structure theory of non-collapsed Kähler Einstein manifolds. As applications, we prove the Hamilton-Tian conjecture and the partial-$C^0$-conjecture of Tian.

We added three appendices and provided more details based on requests and suggestions from interested readers

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Cited by in corpus (30)

• Sasaki-Einstein metrics and K-stability
• KAWA lecture notes on the Kähler-Ricci flow
• The Ricci flow on the sphere with marked points
• The inverse Monge-Ampere flow and applications to Kahler-Einstein metrics
• Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below, II
• Some refinements of the partial $C^0$ estimate
• The local entropy along Ricci flow---Part A: the no-local-collapsing theorems
• Remarks of weak-compactness along Kahler Ricci flow
• Ricci flow on Orbifold
• Degeneration of Kähler-Ricci solitons
• New curvature flows in complex geometry
• Geometric flow, Multiplier ideal sheaves and Optimal destabilizer for a Fano manifold
• Singular limits of Kähler-Ricci flow on Fano $G$-manifolds
• Pluricomplex Green's functions and Fano manifolds
• Collapsing geometry with Ricci curvature bounded below and Ricci flow smoothing
• The extension problem of the mean curvature flow (I)
• On Feldman-Ilmanen-Knopf conjecture for the blow-up behavior of the Kahler Ricci flow
• Tian's partial $C^0$-estimate implies Hamilton-Tian's conjecture
• On Ilmanen's multiplicity-one conjecture for mean curvature flow with type-I mean curvature
• Notes on Ricci flows with collapsing initial data (I): Distance distortion
• The (logarithmic) Sobolev inequalities along geometric flow and applications
• The complex Monge-Ampere equation on compact Kaehler manifolds
• The Partial $C^0$-estimate along a general continuity path and applications
• On the structure of Ricci shrinkers
• The Kähler-Ricci flow and quantitative bounds for Donaldson-Futaki invariants of optimal degenerations
• An explicit estimate of the Bergman kernel for positive line bundles
• Finiteness of $\mathbb{Q}$-Fano compactifications of semisimple group with Kähler-Einstein metrics
• The Rigidity of Ricci shrinkers of dimension four
• A compactness result for Fano manifolds and Kähler Ricci flows
• Degeneration of shrinking Ricci solitons