Mathematical Research Letters

Volume 24 (2017)

Number 6

Weak solutions of the Chern–Ricci flow on compact complex surfaces

Pages: 1819 – 1844



Xiaolan Nie (Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, China)


In this note, we prove the existence of weak solutions of the Chern–Ricci flow through blow downs of exceptional curves, as well as backwards smooth convergence away from the exceptional curves on compact complex surfaces. The smoothing property for the Chern–Ricci flow is also obtained on compact Hermitian manifolds of dimension $n$ under a mild assumption.

Received 18 January 2017

Accepted 4 May 2017

Published 29 January 2018