Mathematical Research Letters

Volume 26 (2019)

Number 6

The Kähler–Ricci flow on pseudoconvex domains

Pages: 1603 – 1627



Huabin Ge (School of Mathematics, Renmin University of China, Beijing, China)

Aijin Lin (Department of Mathematics, National University of Defense Technology, Changsha, China)

Liangming Shen (School of Mathematical Sciences, Beihang University, Beijing, China)


We establish the existence of the Kähler–Ricci flow on pseudoconvex domains with general initial metrics without curvature bounds. We could show that the evolving metric is simultaneously complete, and the corresponding normalized Kähler–Ricci flow converges to the complete Kähler–Einstein metric, which generalizes Topping’s simultaneously complete Ricci flow on surfaces to high dimensional case.

The first author is partially supported by the NSFC Grant No. 11871094 and the second author is supported by National Natural Science Foundation of China under Grant No. 11401578 and Scientific Research Program Funds of NUDT under Grant No. ZK18-03-30.

Received 26 March 2018

Accepted 14 October 2019

Published 6 March 2020