we explain a recent work with huang where we combine various results in complex analysis including fefferman's invariant theory, the chern-moser theory, the cheng-yau solution of kahler-einstein metrics, to provide an affirmative solution of a conjecture posed by cheng-yau. the conjecture stated that the bergman metric of a bounded strongly pseudoconvex domain is einstein if and only if the domain is holomorphically equivalent to the ball.