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The Levi problem on strongly pseudoconvex G-bundles

2008/02/29 by Joe J. Perez
Mathematics · #Advanced Algebra and Geometry #Complex manifold #Differential geometry #Geometry and complex manifolds #Holomorphic and Operator Theory #Holomorphic function #Holonomy #Manifold (fluid mechanics) #Principal bundle #Space (punctuation) #Unimodular matrix #math.CV #math.RT #msc:32E40 #msc:32W05 #msc:43A30

paper · pdf · doi:10.1007/s10455-009-9170-z

published as Ann. Glob. Anal. Geom. (2010), v.37, 1--20 · 19 pages--Corrects earlier versions

arxiv created 2008/10/13 · openalex publication_date 2009/07/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Let G be a unimodular Lie group, X a compact manifold with boundary, and M the total space of a principal bundle G→ M→ X so that M is also a strongly pseudoconvex complex manifold. In this work, we show that if G acts by holomorphic transformations satisfying a local property, then the space of square-integrable holomorphic functions on M is infinite G-dimensional.

Citations