Pluripotential Kähler–Ricci flows

2018/10/04 by Vincent Guedj, Hoang Chinh Lu, Chinh H. Lu +2
Mathematics · #Algebraic Geometry and Number Theory #Degenerate energy levels #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Gravitational singularity #Mathematical analysis #Mathematical physics #Mathematics #Parabolic partial differential equation #Partial differential equation #Physics #Pure mathematics #Ricci curvature #Ricci flow #math.AP #math.CV #math.DG

paper · pdf · doi:10.2140/gt.2020.24.1225

published as Geom. Topol. 24 (2020) 1225-1296

arxiv created 2018/10/04 · openalex publication_date 2020/09/30 · arxiv updated 2020/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We develop a parabolic pluripotential theory on compact Kähler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge–Ampère equations. We provide a parabolic analogue of the celebrated Bedford–Taylor theory and apply it to the study of the Kähler–Ricci flow on varieties with log terminal singularities.

Citations

• Three-manifolds with positive Ricci curvature
• Birational Geometry of Algebraic Varieties
• On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I
• Stability of solutions to complex Monge-Ampère equations in big cohomology classes