Regularity of Kähler-Ricci flows on Fano manifolds

Abstract

In this paper, we will establish a regularity theory for the Kähler-Ricci flow on Fano $n$-manifolds with Ricci curvature bounded in $L^p$-norm for some $p>n$. Using this regularity theory, we will also solve a long-standing conjecture for dimension 3. As an application, we give a new proof of the Yau-Tian-Donaldson conjecture for Fano 3-manifolds. The results have been announced in \cite{TiZh12b}.

Proof of results announced in arXiv:1304.2651v1

References in corpus (14)

• K-stability and Kähler-Einstein metrics
• Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof
• The logarithmic Sobolev inequality along the Ricci flow
• Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry, II
• Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2 π
• Convergence of a Kähler-Ricci flow
• Stable Pairs and Coercive Estimates for The Mabuchi Functional
• Supremum of Perelman's entropy and Kähler-Ricci flow on a Fano manifold
• Degeneration of Kahler-Ricci solitons on Fano manifolds
• A Numerical Criterion for K-Energy maps of Algebraic Manifolds
• On the uniqueness of asymptotic limits of the Ricci flow
• Degeneration of Kähler-Ricci solitons
• Regularity of Kähler-Ricci flow
• Decomposition Theory

Cited by in corpus (7)

• Space of Ricci flows (II)
• Complex optimal transport and the pluripotential theory of Kähler-Ricci solitons
• Extremal Kähler metrics
• Convergence of Kähler-Ricci flow on lower dimensional algebraic manifolds of general type
• On the Kahler Ricci flow on projective manifolds of general type
• Local Sobolev Constant Estimate for Integral Ricci Curvature Bounds
• New Volume Comparison results and Applications to degeneration of Riemannian metrics