Hausdorff-(2n-2) dimensional measure zero set and compactness of the ∂-Neumann operator on (0,n-1) forms

2019/03/11 by Yue Zhang, Zhang, Yue
Computer Science · Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Complex Variables (math.CV) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1903.04112

openalex publication_date 2019/03/11 · openalex created_date 2019/03/22 · openalex updated_date 2026/07/28

Abstract

By using a variant Property (P_q) of Catlin, we discuss the relation of small set of weakly pseudoconvex points on the boundary of pseudoconvex domain and compactness of the ∂-Neumann operator. In particular, we show that if the Hausdorff (2n-2)-dimensional measure of the weakly pseudoconvex points on the boundary of a smooth bounded pseudoconvex domain is zero, then the ∂-Neumann operator N_n-1 is compact on (0,n-1)-level L²-integrable forms.

Related

• Compactness of the ∂-Neumann operator on the intersection of two domains
• 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 weighted (0,q)- forms
• Observations regarding compactness in the ∂-Neumann problem