The Michigan Mathematical Journal
- Michigan Math. J.
- Advance publication (2019), 16 pages.
Topology of Kähler Manifolds with Weakly Pseudoconvex Boundary
We study Kähler manifolds-with-boundary, not necessarily compact, with weakly pseudoconvex boundary, each component of which is compact. If such a manifold has boundary components (possibly ), then it has the first Betti number at least , and the Levi form of any boundary component is zero. If has pseudoconvex boundary components and at least one nonparabolic end, then the first Betti number of is at least . In either case, any boundary component has a nonvanishing first Betti number. If has one pseudoconvex boundary component with vanishing first Betti number, then the first Betti number of is also zero. Especially significant are applications to Kähler ALE manifolds and to Kähler 4-manifolds. This significantly extends prior results in this direction (e.g., those of Kohn and Rossi) and uses substantially simpler methods.
Michigan Math. J., Advance publication (2019), 16 pages.
Received: 14 August 2017
Revised: 4 April 2019
First available in Project Euclid: 23 July 2019
Permanent link to this document
Digital Object Identifier
Primary: 53C55, 53C23, 31C12, 31C10, 58J99
Weber, Brian. Topology of Kähler Manifolds with Weakly Pseudoconvex Boundary. Michigan Math. J., advance publication, 23 July 2019. doi:10.1307/mmj/1563847454. https://projecteuclid.org/euclid.mmj/1563847454