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arXiv · 2510.13278

Rigidity of complete Kähler-Einstein metrics under cscK perturbations

Zehao Sha
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Abstract

In this paper, we study constant scalar curvature Kähler (cscK) metrics on complete non-compact Kähler--Einstein manifolds. We give sufficient conditions under which a cscK perturbation of a Kähler--Einstein metric must remain Kähler--Einstein. As a model case, we prove that the Bergman metric on a bounded strictly pseudoconvex domain is Kähler--Einstein whenever it has constant scalar curvature. In particular, combined with Huang--Xiao's resolution of Cheng's conjecture, this yields the ball characterization for smooth bounded strictly pseudoconvex domains.

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Zehao Sha. 2026-04-13. Rigidity of complete Kähler-Einstein metrics under cscK perturbations. https://arxiv.org/abs/2510.13278

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