Geometric Constructions of Extremal Metrics on Complex Manifolds

DOI10.1007/978-3-319-05254-0_17zbMath1333.32029OpenAlexW1009710520MaRDI QIDQ2948986

Claudio Arezzo

Publication date: 7 October 2015

Published in: Trends in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-05254-0_17

zbMATH Keywords

complex manifoldscritical metricsKähler constant scalar curvature metrics

Mathematics Subject Classification ID

Kähler manifolds (32Q15) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Critical metrics (58E11) Kähler-Einstein manifolds (32Q20)

Cites Work

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• On blowing up extremal Kähler manifolds
• Extremal metrics on blowups
• Relative K-stability of extremal metrics
• Monge-Ampère equations in big cohomology classes
• Existence and deformation theory for scalar-flat Kähler metrics on compact complex surfaces
• Blowing up Kähler manifolds with constant scalar curvature. II.
• On Calabi's conjecture for complex surfaces with positive first Chern class
• Construction of Kähler surfaces with constant scalar curvature
• Blowing up and desingularizing constant scalar curvature Kähler manifolds
• Smoothing singular constant scalar curvature Kähler surfaces and minimal Lagrangians
• K-stability of constant scalar curvature Kähler manifolds
• Geometry of Kähler metrics and foliations by holomorphic discs
• Conformal deformation of a Riemannian metric to constant scalar curvature
• A remark on extremal Kähler metrics
• Stability of vector bundles and extremal metrics
• The existence of Kähler-Einstein metrics on manifolds with positive anticanonical line bundle and a suitable finite symmetry group
• Einstein-Kähler forms, Futaki invariants and convex geometry on toric Fano varieties
• The construction of ALE spaces as hyper-Kähler quotients
• Kähler-Einstein metrics and integral invariants
• Extremal Kähler metrics and complex deformation theory
• Kähler-Einstein metrics with positive scalar curvature
• Scalar curvature and projective embeddings. I
• An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds. I.
• Einstein metrics and complex singularities
• Kähler--Ricci solitons on toric manifolds with positive first Chern class
• A new method of constructing scalar-flat Kähler surfaces
• On the scalar curvature of complex surfaces
• Minimal resolutions of Gorenstein orbifolds in dimension three
• Kähler metrics of constant scalar curvature on bundles over \({\mathbb{C}}{\mathbb{P}}_{n-1}\)
• Geometric flows and Kähler reduction
• Lower bounds on the Calabi functional
• On conformally Kähler, Einstein manifolds
• Sur la Structure du Groupe d’Homéomorphismes Analytiques d’une Certaine Variété Kaehlérinne
• Scalar-flat Kähler metrics on blown-up ruled surfaces.
• Extremal metrics and K-stability
• Kahler geometry on toric manifolds, and some other manifolds with large symmetry
• Unstable blowups
• The Kähler-Ricci flow and K-polystability
• Log canonical thresholds of smooth Fano threefolds
• Métriques kählériennes et fibrés holomorphes
• Deformations of nodal Kähler-Einstein Del Pezzo surfaces with discrete automorphism groups
• Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities
• Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches \boldmath2𝜋 and completion of the main proof

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