Propagation of regularity for solutions of the Kohn Laplacian in a flat boundary

2009/08/14 by Luca Baracco, Baracco, Luca, Tran Vu Khanh +3 · 1 citation
Mathematics · #32F10 #32F20 #32N15 #32T25 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:32F10 #msc:32F20 #msc:32N15 #msc:32T25

paper · pdf · doi:10.48550/arxiv.0908.2149

arxiv created 2009/08/14 · openalex publication_date 2009/08/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that CR lines in an exponentially degenerate boundary are propagators of holomorphic extension. This explains, in the context of the CR geometry, why in this situation the induced Kohn-Laplacian \Box_b is not hypoelliptic according to recent work by Christ.

Cited by

• Hypoellipticity of the ∂-Neumann problem by means of subelliptic multipliers

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