Existence of coupled Kähler–Einstein metrics using the continuity method

DOI10.1142/S0129167X18500416MaRDI QIDQ4565067

Vamsi Pritham Pingali

Publication date: 7 June 2018

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.02047

zbMATH Keywords

a priori estimatescontinuity methodFano manifoldscoupled Kähler-Einstein metrics

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Kähler-Einstein manifolds (32Q20)

Related Items (8)

Deformation for coupled Kähler-Einstein metrics ⋮ Calabi type functionals for coupled Kähler-Einstein metrics ⋮ Anticanonically balanced metrics and the Hilbert-Mumford criterion for the \(\delta_m\)-invariant of Fujita-Odaka ⋮ Geometric quantization of coupled Kähler-Einstein metrics ⋮ Coupled complex Monge-Ampère equations on Fano horosymmetric manifolds ⋮ Coupled Kähler-Ricci solitons on toric Fano manifolds ⋮ Coupled Sasaki-Ricci solitons ⋮ Residue formula for an obstruction to coupled Kähler-Einstein metrics

Cites Work

• Kähler-Einstein metrics along the smooth continuity method
• The complex Monge-Ampère equation on compact Kähler manifolds
• The complex Monge-Ampère equation
• On the \(C^{2,\alpha}\)-regularity of the complex Monge-Ampère equation
• Bimetric gravity from ghost-free massive gravity
• On uniform estimate in Calabi-Yau theorem
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• Coupled Kähler–Einstein Metrics
• 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

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