On compact subsets possessing strictly plurisubharmonic functions

2020/04/30 by Nikolay Shcherbina, N. V. Shcherbina
Mathematics · #Compact space #Complex manifold #Function (biology) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #Manifold (fluid mechanics) #Neighbourhood (mathematics) #math.CV #msc:32U05

paper · pdf · doi:10.1070/im9059

15 pages. Comments welcome!

openalex created_date 2020/05/13 · arxiv created 2020/08/02 · openalex publication_date 2020/11/03 · arxiv updated 2021/08/11 · openalex updated_date 2026/08/05

Abstract

Abstract We give a geometric condition on a compact subset of a complex manifold which is necessary and sufficient for the existence of a smooth strictly plurisubharmonic function defined in a neighbourhood of this set.

Citations

• The Levi problem for complex spaces
• On Levi's Problem and the Imbedding of Real-Analytic Manifolds
• An intrinsic characterization of Kähler manifolds
• Levi problem in complex manifolds
• The Levi problem for complex spaces II