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


Takeo Ohsawa (Graduate School of Mathematics, Nagoya University, Chikusaku Furocho, Nagoya, Japan)


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


Received 19 October 2020

Accepted 11 March 2021

Published 13 May 2022