Observations regarding compactness in the ∂-Neumann problem

2008/06/23 by Mehmet Çelik, Mehmet Çeli̇k, Çelik, Mehmet +3
Mathematics · #32W05 #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #advanced mathematical theories #math.CV #msc:32W05

paper · pdf · doi:10.48550/arxiv.0806.3783

arxiv created 2008/06/23 · openalex publication_date 2008/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

We show that compactness of the ∂-Neumann operator is independent of the metric, and we give a new proof of this independence for subellipticity. We define an abstract obstruction to compactness, namely the common zero set of all the compactness multipliers, and we identify this subset of the boundary for convex domains in ℂⁿ and for complete Hartogs domains in ℂ².

Citations

• Equivalence of types and Catlin boundary systems

Related

• Compactness of the ∂-Neumann problem on domains with bounded intrinsic geometry
• Geometric conditions which imply compactness of the ∂-Neumann operator
• Sufficient condition for compactness of the ∂-Neumann operator using the Levi core
• Compactness of the ∂-Neumann operator on the intersection of two domains
• On compactness of the ∂-Neumann operator on Hartogs domains