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Pure and Applied Mathematics Quarterly
Volume 18 (2022)
Number 2
Special issue in honor of Joseph J. Kohn on the occasion of his 90th birthday
Guest Editors: J.E. Fornaess, Stanislaw Janeczko, Duong H. Phong, and Stephen S.T. Yau
On the Levi problem on Kähler manifolds under the negativity of canonical bundles on the boundary
Pages: 763 – 771
DOI: https://dx.doi.org/10.4310/PAMQ.2022.v18.n2.a17
Author
Abstract
It is proved that a bounded $C^2$-smooth pseudoconvex domain $\Omega$ in a Kähler manifold $M$ can be mapped onto a locally closed analytic set in $\mathbb{C}^N$ holomorphically and properly with connected fibers if the canonical bundle of $M$ is negative on a neighborhood of $\partial \Omega$. A similar result is obtained for Zariski open domains in compact manifolds.
2010 Mathematics Subject Classification
32E40
Received 19 October 2020
Accepted 11 March 2021
Published 13 May 2022