On the displacement rigidity of Levi flat hypersurfaces - The case of boundaries of disc bundles over compact Riemann surfaces

2005/11/04 by Klas Diederich, K. Diederich, Takeo Ohsawa +3
Mathematics · #14H30 #30F35 #32G07 #32G08 #32L05 #32V15 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:14H30 #msc:30F35 #msc:32G07 #msc:32G08 #msc:32L05 #msc:32V15

paper · pdf · doi:10.48550/arxiv.math/0511108

9 pages

arxiv created 2005/11/04 · openalex publication_date 2005/11/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Non-existence theorems for Levi flat hypersurfaces have found great interest in the literature. The question next to this that has to be asked is, when existing Levi flat hypersurfaces are at least rigid under deformations. Here, the case of boundaries of disc bundles over certain compact Riemann surfaces is considered.

Related

• Deformations of Levi flat hypersurfaces in complex manifolds
• Boundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry-Mather theory
• Topology and dynamics of Levi-flats in surfaces of general type
• On rigid compact complex surfaces and manifolds
• Levi-flat hypersurfaces and their complement in complex surfaces