Singularities of the Chern–Ricci flow
Abstract
We study the nature of finite time singularities for the Chern-Ricci flow, partially answering a question posed by Tosatti and Weinkove.We show that a solution of degenerate parabolic complex Monge-Ampère equations, starting from arbitrarily positive (1,1)-currents, is smooth outside some analytic subset, generalizing works by Di Nezza and Lu.Moreover, we extend Guedj and Lu's recent approach to establish uniform a priori estimates for degenerate complex Monge-Ampère equations on compact Hermitian manifolds.We apply these results to study the Chern-Ricci flow on log terminal varieties starting from a current with mild singularities.
Fields of Study & Subjects
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Black Holes and Theoretical Physics
Publication details
- Journal / source
- Analysis & PDE
- Volume
- 19
- Issue
- 3
- Pages
- 449–483
- Publication date
- 11 March 2026
- Language
- EN