Coupled complex Monge-Ampère equations on Fano horosymmetric manifolds

DOI10.1016/j.matpur.2020.12.002zbMath1490.53087arXiv1812.07218OpenAlexW3111440784MaRDI QIDQ1983084

Thibaut Delcroix, Jakob Hultgren

Publication date: 15 September 2021

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.07218

zbMATH Keywords

Monge-Ampère equationKähler-Ricci solitonMabuchi metriccoupled Kähler-Einstein metrichorosymmetric manifold

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) Global differential geometry of Hermitian and Kählerian manifolds (53C55) Kähler manifolds (32Q15) Fano varieties (14J45) Kähler-Einstein manifolds (32Q20) Almost homogeneous manifolds and spaces (32M12) Monge-Ampère equations (35J96) Compactifications; symmetric and spherical varieties (14M27)

Related Items (7)

Examples of K-unstable Fano manifolds ⋮ On the Yau‐Tian‐Donaldson Conjecture for Generalized Kähler‐Ricci Soliton Equations ⋮ Calabi type functionals for coupled Kähler-Einstein metrics ⋮ Anticanonically balanced metrics and the Hilbert-Mumford criterion for the \(\delta_m\)-invariant of Fujita-Odaka ⋮ Greatest Ricci lower bounds of projective horospherical manifolds of Picard number one ⋮ Multiplier Hermitian-Einstein metrics on Fano manifolds of KSM-type ⋮ Geometric quantization of coupled Kähler-Einstein metrics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Kähler-Einstein metrics along the smooth continuity method
• Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties
• Fano symmetric varieties with low rank
• Kähler-Einstein metrics on group compactifications
• Valuations des espaces homogènes sphériques. (Valuations of spherical homogeneous spaces)
• Greatest lower bounds on Ricci curvature for toric Fano manifolds
• Groupe de Picard et nombres caractéristiques des variétés sphériques. (Picard group and characteristic numbers of spheric varieties.)
• Kähler--Ricci solitons on toric manifolds with positive first Chern class
• On the \(C^{2,\alpha}\)-regularity of the complex Monge-Ampère equation
• Coupled Sasaki-Ricci solitons
• Kähler geometry of horosymmetric varieties, and application to Mabuchi's K-energy functional
• Coupled Kähler-Ricci solitons on toric Fano manifolds
• Mabuchi metrics and properness of the modified Ding functional
• K-stability of Fano spherical varieties
• Kahler geometry on toric manifolds, and some other manifolds with large symmetry
• Kähler-Ricci solitons on homogeneous toric bundles
• Variétés horosphériques de Fano
• Multiplier Hermitian structures on Kähler manifolds
• Existence of coupled Kähler–Einstein metrics using the continuity method
• Fano threefolds with infinite automorphism groups
• Coupled Kähler–Einstein Metrics
• K‐Stability and Kähler‐Einstein Metrics
• Greatest lower bounds on Ricci curvature of homogeneous toric bundles
• 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 for manifolds with nonvanishing Futaki character
• Kähler-Ricci soliton typed equations on compact complex manifolds with \(c_1(M)>0\).

This page was built for publication: Coupled complex Monge-Ampère equations on Fano horosymmetric manifolds