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

2015/06/21 by Xiuxiong Chen, Chen, Xiuxiong · 5 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1506.06423

openalex publication_date 2015/06/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Stable Pairs and Coercive Estimates for The Mabuchi Functional
• CM Stability and the Generalized Futaki Invariant I
• On the long time behaviour of the Conical Kähler- Ricci flows
• Extremal Kähler metrics

Cited by

• Twisted Calabi functional and twisted Calabi flow
• Calabi flow with bounded L^p scalar curvature (II)
• Rigidity of complete Kähler-Einstein metrics under cscK perturbations
• Twisted and coupled constant scalar curvature Kähler metrics on minimal ruled surfaces
• On uniform log K-stability for constant scalar curvature Kähler cone metrics

Related

• Constant μ-scalar curvature Kähler metric -- formulation and foundational results
• Constant scalar curvature equation and the regularity of its weak solution
• A remark on Kähler metrics of constant scalar curvature on ruled complex surfaces
• Constant Scalar Curvature Kähler Metrics on Resolutions of an Orbifold Singularity of Depth 1
• On the constant scalar curvature Kähler metrics, general automorphism group