Singularities of the Chern–Ricci flow

Dang, Quang-Tuan

doi:10.2140/apde.2026.19.449

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Singularities of the Chern–Ricci flow

Quang-Tuan Dang

Vol. 19 (2026), No. 3, 449–483

DOI: 10.2140/apde.2026.19.449

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.

Keywords

Monge–Ampère equations, Chern–Ricci flow, singularities

Mathematical Subject Classification

Primary: 53E30

Secondary: 32U20, 32W20

Milestones

Received: 8 January 2024

Revised: 19 February 2025

Accepted: 14 April 2025

Published: 11 March 2026

Authors

Quang-Tuan Dang
The Abdus Salam International Centre for Theoretical Physics (ICTP) Trieste, Italy	Yau Mathematical Sciences Center Tsinghua University Beijing China

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Vol. 19, No. 3, 2026