Extremal Kähler metrics

Abstract

This paper is a survey of some recent progress on the study of Calabi's extremal Kähler metrics. We first discuss the Yau-Tian-Donaldson conjecture relating the existence of extremal metrics to an algebro-geometric stability notion and we give some example settings where this conjecture has been established. We then turn to the question of what one expects when no extremal metric exists.

17 pages, 4 figures. Contribution to the proceedings of the 2014 ICM

References in corpus (8)

• Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof
• CM Stability and the Generalized Futaki Invariant I
• K-stability of constant scalar curvature polarization
• Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry, II
• Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2 π
• Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities
• Kahler-Einstein metrics and stability
• Degeneration of Kahler-Ricci solitons on Fano manifolds

Cited by in corpus (3)

• Non-equilibrium dynamics and $Ad{S}_4$ Robinson-Trautman
• On the existence of constant scalar curvature Kähler metric: a new perspective
• HCMU metrics with cusp singularities and conical singularities