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

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

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

Full Text (PDF format)

Received 19 October 2020

Accepted 11 March 2021

Published 13 May 2022