#### Vol. 288, No. 2, 2017

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On bisectional nonpositively curved compact Kähler–Einstein surfaces

### Daniel Guan

Vol. 288 (2017), No. 2, 343–353
##### Abstract

We prove a conjecture on the pinching of the bisectional curvature of nonpositively curved Kähler–Einstein surfaces. We also prove that any compact Kähler–Einstein surface $M$ is a quotient of the complex two-dimensional unit ball or the complex two-dimensional plane if $M$ has nonpositive Einstein constant and, at each point, the average holomorphic sectional curvature is closer to the minimum than to the maximum.

##### Keywords
Kähler–Einstein metrics, compact complex surfaces, bisectional curvature, pinching of the curvatures
##### Mathematical Subject Classification 2010
Primary: 32M15, 32Q20, 53C21, 53C55