Rigidity of complete Kähler-Einstein metrics under cscK perturbations
Authors
Zehao Sha
Abstract
In this paper, we study constant scalar curvature Kähler (cscK) metrics on a complete non-compact Kähler-Einstein manifold. We give a sufficient condition under which any cscK perturbation of the Kähler-Einstein metric remains Kähler-Einstein. As a model case, we extend Huang-Xiao's resolution of Cheng's conjecture if the Bergman metric has constant scalar curvature on bounded strictly pseudoconvex domains with smooth boundary.
