On the existence of constant scalar curvature Kähler metric: a new perspective

DOI10.1007/s40316-017-0086-xzbMath1401.53028arXiv1506.06423OpenAlexW2964005858MaRDI QIDQ1616061

Xiuxiong Chen

Publication date: 31 October 2018

Published in: Annales Mathématiques du Québec (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.06423

zbMATH Keywords

Monge-Ampère equationnew continuity pathtwisted cscK metric

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Elliptic equations on manifolds, general theory (58J05) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

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Geometric pluripotential theory on Sasaki manifolds ⋮ A Yau-Tian-Donaldson correspondence on a class of toric fibrations ⋮ Constant scalar curvature Kähler metrics on ramified Galois coverings ⋮ On the constant scalar curvature Kähler metrics (I)—A priori estimates ⋮ On the constant scalar curvature Kähler metrics (II)—Existence results ⋮ Uniqueness of constant scalar curvature Kähler metrics with cone singularities. I: Reductivity ⋮ Compactness of Kähler metrics with bounds on Ricci curvature and \({\mathcal{I}}\) functional ⋮ Stable maps in higher dimensions ⋮ On Calabi’s extremal metric and properness ⋮ Stability and Hölder regularity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds

Cites Work

• Unnamed Item
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• Weak solutions to degenerate complex Monge-Ampère flows. II
• K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics
• Uniqueness and short time regularity of the weak Kähler-Ricci flow
• Moduli spaces of critical Riemannian metrics with \(L^{\frac{n}{2}}\) norm curvature bounds
• Kähler-Einstein metrics on Fano surfaces
• The Mabuchi geometry of finite energy classes
• Minimizing weak solutions for Calabi's extremal metrics on toric manifolds
• Space of Kähler metrics. III: On the lower bound of the Calabi energy and geodesic distance
• K-stability of constant scalar curvature Kähler manifolds
• Geometry of Kähler metrics and foliations by holomorphic discs
• Some symplectic geometry on compact Kähler manifolds. I
• Extremal Kähler metrics and complex deformation theory
• Kähler-Einstein metrics with positive scalar curvature
• Scalar curvature and projective embeddings. I
• Sir Michael Atiyah. A great mathematician of the twentieth century. Special issue dedicated to Sir Michael Atiyah on the occasion of his 70th birthday
• The space of Kähler metrics.
• A new parabolic flow in Kähler manifolds
• Convergence of the \(J\)-flow on Kähler surfaces
• Twisted constant scalar curvature Kähler metrics and Kähler slope stability
• The J-flow and stability
• Regularizing properties of the twisted Kähler-Ricci flow
• A thermodynamical formalism for Monge-Ampère equations, Moser-Trudinger inequalities and Kähler-Einstein metrics
• A remark on conical Kähler-Einstein metrics
• Long time existence of minimizing movement solutions of Calabi flow
• An obstruction to the existence of constant scalar curvature Kähler metrics
• The \(J\)-flow on Kähler surfaces: a boundary case
• Weak solutions to degenerate complex Monge-Ampère flows. I
• Constant scalar curvature Kähler metrics on fibred complex surfaces
• Moduli spaces of critical Riemannian metrics in dimension four
• The partial 𝐶⁰-estimate along the continuity method
• Space of Kähler Metrics (V) – Kähler Quantization
• Tian’s properness conjectures and Finsler geometry of the space of Kähler metrics
• On the weak Kähler-Ricci flow
• Greatest lower bounds on the Ricci curvature of Fano manifolds
• On the Calabi flow
• On the construction of Nadel multiplier ideal sheaves and the limiting behavior of the Ricci flow
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• Uniform Stability of Twisted Constant Scalar Curvature Kähler Metrics
• Kähler Metrics with Cone Singularities Along a Divisor
• Convexity of the 𝐾-energy on the space of Kähler metrics and uniqueness of extremal metrics
• On the convergence and singularities of the J‐Flow with applications to the Mabuchi energy
• Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities
• Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than \boldmath2𝜋
• Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches \boldmath2𝜋 and completion of the main proof
• Kähler-Einstein metrics with edge singularities