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.

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