Communications in Analysis and Geometry

Volume 21 (2013)

Number 2

$U(n)$-invariant Kähler–Ricci flow with non-negative curvature

Pages: 251 – 294



Bo Yang (Department of Mathematics, University of California at San Diego)

Fangyang Zheng (Center for Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang, China)


It is interesting to know the existence of the Kähler–Ricci flow on complete non-compact Kähler manifolds with non-negative holomorphic bisectional curvature. In this paper, we study $U(n)$-invariant Kähler–Ricci flow on $\mathbb{C}^n$ with non-negative curvature. Motivated by the recent work of Wu and the second named author, we also study examples of $U(n)$-invariant complete Kähler metrics on $\mathbb{C}^{n}$ with positive and unbounded curvature.

Published 9 April 2013