The K"ahler-Ricci flow with Log Canonical Singularities

2019/06/11 by Albert Chau, Huabin Ge, Chau, Albert +5
Mathematics · Physics and Astronomy · #53C44 #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1906.04343

openalex publication_date 2019/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the existence of the K"ahler-Ricci flow on projective varieties with log canonical singularities. This generalizes some of the existence results of Song-Tian \citeST3 in case of projective varieties with klt singularities. We also prove that the normalized K"ahler-Ricci flow will converge to the \ka-Einstein metric with negative Ricci curvature on semi-log canonical models in the sense of currents. Finally we also construct K"ahler-Ricci flow solutions performing divisorial contractions and flips with log canonical singularities.

Citations

• Introduction to the log minimal model program for log canonical pairs
• Relative volume comparison of Ricci Flow and its applications

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