On strictly pseudoconvex domains with Kähler-Einstein Bergman metrics
The authors prove that a smoothly bounded, strictly pseudoconvex domain in \(\mathbb{C}^n\) with Bergman metric that is Kähler-Einstein must be the ball. This adds a nice new result to the roster of intrinsic characterizations of the ball that have been discovered in the past twenty years. Key to the arguments in the paper is the following result of Burns: If a strongly pseudoconvex domain has Bergman kernel asymptotic expansion of Fefferman with no logarithmic term at any boundary point then the domain is the ball.
scientific article; zbMATH DE number 1117491