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Title: Bergman–Einstein metrics, a generalization of Kerner’s theorem and Stein spaces with spherical boundaries
Abstract We give an affirmative solution to a conjecture of Cheng proposed in 1979which asserts that the Bergman metric of a smoothly bounded stronglypseudoconvex domain in {\mathbb{C}^{n},n\geq 2} , is Kähler–Einsteinif and only if the domain is biholomorphic to the ball. We establisha version of the classical Kerner theorem for Stein spaces withisolated singularities which has an immediate application toconstruct a hyperbolic metric over a Stein space with a sphericalboundary.  more » « less
Award ID(s):
1665412 2000050 1800549
PAR ID:
10234231
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Journal für die reine und angewandte Mathematik (Crelles Journal)
Volume:
2021
Issue:
770
ISSN:
0075-4102
Page Range / eLocation ID:
183 to 203
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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