Tian's partial \(C^0\)-estimate implies Hamilton-Tian's conjecture

DOI10.1016/j.aim.2021.107619zbMath1479.53105arXiv2002.05501OpenAlexW3122157122WikidataQ113881036 ScholiaQ113881036MaRDI QIDQ2656131

Xiaohua Zhu, Feng Wang

Publication date: 10 March 2021

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.05501

zbMATH Keywords

Fano manifoldsKähler-Ricci flowHamilton-Tian's conjectureTian's partial \(C^0\)-estimate

Mathematics Subject Classification ID

Critical metrics (58E11) Kähler-Einstein manifolds (32Q20) Positive curvature complex manifolds (32Q10) Ricci flows (53E20)

Related Items (9)

On the lower boundedness of modified \(K\)-energy ⋮ Algebraic uniqueness of Kähler-Ricci flow limits and optimal degenerations of Fano varieties ⋮ Kähler-Ricci flow on Fano manifolds ⋮ The asymptotic behavior of Bergman kernels ⋮ Kähler-Ricci flow on rational homogeneous varieties ⋮ Singular Kähler-Einstein metrics on \(\mathbb{Q}\)-Fano compactifications of Lie groups ⋮ Geometric methods of complex analysis. Abstracts from the workshop held May 16--22, 2021 (hybrid meeting) ⋮ Uniformly strong convergence of Kähler-Ricci flows on a Fano manifold ⋮ Kähler-Ricci flow for deformed complex structures

Cites Work

• Unnamed Item
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• Bergman kernel along the Kähler-Ricci flow and Tian's conjecture
• Kähler-Einstein metrics along the smooth continuity method
• Partial \(C^0\)-estimate for Kähler-Einstein metrics
• Conical Kähler-Einstein metrics revisited
• Gromov-Hausdorff limits of Kähler manifolds and algebraic geometry
• Regularity of Kähler-Ricci flows on Fano manifolds
• On Calabi's conjecture for complex surfaces with positive first Chern class
• A new capacity for plurisubharmonic functions
• The Ricci flow on the 2-sphere
• On a set of polarized Kähler metrics on algebraic manifolds
• Logarithmic Sobolev inequalities and the spectrum of Schrödinger operators
• Kähler-Einstein metrics with positive scalar curvature
• On the structure of spaces with Ricci curvature bounded below. I
• Uniqueness of Kähler-Ricci solitons.
• Convergence of Ricci flows with bounded scalar curvature
• Bergman kernels for a sequence of almost Kähler-Ricci solitons
• Kähler-Ricci flow, Kähler-Einstein metric, and K-stability
• On the singularities of spaces with bounded Ricci curvature
• On the \(C^{2,\alpha}\)-regularity of the complex Monge-Ampère equation
• Uniformly strong convergence of Kähler-Ricci flows on a Fano manifold
• Space of Ricci flows. II. Part B: Weak compactness of the flows
• The Kähler-Ricci flow and optimal degenerations
• On the Kähler-Ricci flow near a Kähler-Einstein metric
• A Brunn-Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry
• Bounds on volume growth of geodesic balls under Ricci flow
• Stability of Kähler-Ricci flow on a Fano manifold
• Kähler-Einstein metrics and the Kähler-Ricci flow on log Fano varieties
• The partial 𝐶⁰-estimate along the continuity method
• Perelman’s entropy and Kähler-Ricci flow on a Fano manifold
• Existence of Einstein Metrics on Fano Manifolds
• Singular Kähler-Einstein metrics
• SPACE OF RICCI FLOWS (II)—PART A: MODULI OF SINGULAR CALABI–YAU SPACES
• Convergence of Kähler-Ricci flow
• BOUNDING SCALAR CURVATURE AND DIAMETER ALONG THE KÄHLER RICCI FLOW (AFTER PERELMAN)
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• On the Kähler–Ricci Flows Near the Mukai–Umemura 3-Fold
• Convergence of the Kähler–Ricci flow on Fano manifolds
• K‐Stability and Kähler‐Einstein Metrics
• A Uniform Sobolev Inequality Under Ricci Flow
• Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities

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