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In this note we explain that the conjecture of the pinching of the bisectional curvature mentioned in [HGY] and [CHY] is proved by a combination of the arguments from the proofs of the Theorem 1.2 in [CHY], the Theorem 2 in [HGY] and the Proposition 4 in [SY]. Moreover, we 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 (1) M has nonpositive Einstein constant and (2) at each point, the averagedoi:10.2140/pjm.2017.288.343 fatcat:ijzxzeiayzeabmfrj5622grgma