Hartogs Type Theorems for CR L² functions on Coverings of Strongly Pseudoconvex Manifolds

2005/12/09 by Alexander Brudnyi, Brudnyi, Alexander
Mathematics · #32A40 #32V25 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.math/0512185

openalex publication_date 2005/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an analog of the classical Hartogs extension theorem for CR L² functions defined on boundaries of certain (possibly unbounded) domains on coverings of strongly pseudoconvex manifolds. Our result is related to a problem posed in the paper of Gromov, Henkin and Shubin [GHS] on holomorphic L₂ functions on coverings of pseudoconvex manifolds.

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