Complex tangential flows and compactness of the ∂- Neumann operator

2006/07/26 by Samangi Munasinghe, Munasinghe, Samangi, Emil J. Sträube +2
Mathematics · #32W05 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #math.AP #math.CV #msc:32W05

paper · pdf · doi:10.48550/arxiv.math/0607685

9 pages

arxiv created 2006/07/26 · openalex publication_date 2006/07/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide geometric conditions on the set of boundary points of infinite type of a smooth bounded pseudoconvex domain in ℂⁿ which imply that the ∂-Neumann operator is compact. These conditions are formulated in terms of certain short time flows in suitable complex tangential directions. It is noteworthy that compactness is not established via the known potential theoretic sufficient conditions. Our results generalize to ℂⁿ the corresponding \mathbb C² results due to the second author.

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