Communications in Analysis and Geometry

Volume 24 (2016)

Number 3

On complete constant scalar curvature Kähler metrics with Poincaré–Mok–Yau asymptotic property

Pages: 521 – 557



Jixiang Fu (Institute of Mathematics, Fudan University, Shanghai, China)

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)

Wubin Zhou (Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China)


Let $X$ be a compact Kähler manifold and $S$ a subvariety of $X$ with higher co-dimension. The aim is to study complete constant scalar curvature Kähler metrics on non-compact Kähler manifold $X-S$ with Poincaré–Mok–Yau asymptotic property (see Definition 1.1). In this paper, the methods of Calabi ansatz and the moment construction are used to provide some special examples of such metrics.

Published 22 June 2016