PLURIPOLAR SETS, REAL SUBMANIFOLDS AND PSEUDOHOLOMORPHIC DISCS

2018/07/25 by Alexandre Sukhov, ALEXANDRE SUKHOV · 2 citations
Mathematics · #Boundary (topology) #Complex manifold #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #Kähler manifold #Manifold (fluid mechanics) #Measure (data warehouse) #Submanifold #math.CV

paper · pdf · doi:10.1017/s1446788719000119

published as J. Aust. Math. Soc. 109 (2020) 270-288 · arXiv admin note: text overlap with arXiv:1807.02645

arxiv created 2018/07/25 · openalex created_date 2018/08/03 · openalex publication_date 2019/04/08 · arxiv updated 2020/08/26 · openalex updated_date 2026/08/05

Abstract

We prove that a compact subset of full measure on a generic submanifold of an almost complex manifold is not a pluripolar set. Several related results on boundary behavior of plurisubharmonic functions are established. Our approach is based on gluing a family of complex discs to a generic manifold along a boundary arc and could admit further applications.

Citations

• Discs and boundary uniqueness for psh functions on almost complex manifolds

Cited by

• On the Fatou theorem for d_J-bar subsolutions in wedges
• On boundary properties of asymptotically holomorphic functions