Sobolev regularity for the $\overline\partial$-Neumann operator and transverse vector fields

TL;DR

This paper introduces a new sufficient condition for the exact regularity of the ar-Neumann operator on certain pseudoconvex domains, using transverse vector fields, inspired by Zhang's compactness condition.

Contribution

It provides a novel regularity criterion for the ar-Neumann operator based on transverse vector fields, extending previous compactness-based conditions.

Findings

New sufficient condition for ar-Neumann regularity

Utilizes transverse vector fields in the analysis

Extends Zhang's compactness condition framework

Abstract

On a bounded smooth pseudoconvex domain in $\mathbb{C}^n$ with $n >2$, inspired by the compactness condition introduced by Yue Zhang, we present the new sufficient condition for the exact regularity of the $\overline\partial$-Neumann operator via the transverse vector fields.