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

Abstract

In this paper, we report a "new" continuity path which links the constant scalar curvature equation to a second order elliptic equation. This is largely an expository article where we describes various aspects of geometry and analysis associated with path.

References in corpus (7)

• Extremal metrics on blow ups
• CM Stability and the Generalized Futaki Invariant I
• On deformation of extremal metrics
• On the long time behaviour of the Conical Kähler- Ricci flows
• Extremal Kähler metrics
• Stable Pairs and Coercive Estimates for The Mabuchi Functional
• Approximation of weak geodesics and subharmonicity of Mabuchi energy

Cited by in corpus (13)

• On the constant scalar curvature Kähler metrics, existence results
• On the constant scalar curvature Kähler metrics, general automorphism group
• Existence of twisted constant scalar curvature Kähler metrics with a large twist
• On the constant scalar curvature Kähler metrics, apriori estimates
• On deformation of extremal metrics
• Deformations from a given Kähler metric to a twisted cscK metric
• Constant scalar curvature equation and the regularity of its weak solution
• Monge-Ampère operators, energy functionals, and uniqueness of Sasaki-extremal metrics
• Construction of constant scalar curvature Kähler cone metrics
• Conic singularities metrics with prescribed scalar curvature: a priori estimates for normal crossing divisors
• The Calabi flow with rough initial data
• Compactness of Kähler metrics with bounds on Ricci curvature and I functional
• About J-flow, J-balanced metrics, uniform J-stability and K-stability