Subellipticity of the $\bar\partial$-Neumann problem on a weakly $q$-pseudoconvex/concave domain

TL;DR

This paper establishes sufficient conditions for subelliptic estimates in the ar-Neumann problem on weakly q-pseudoconvex or concave domains, extending Catlin's techniques to non-pseudoconvex settings.

Contribution

It introduces new criteria for subellipticity applicable to broader classes of domains beyond pseudoconvex ones, expanding the theoretical framework.

Findings

Provides a sufficient condition for subelliptic estimates on weakly q-pseudoconvex/concave domains.

Extends Catlin's methods to non-pseudoconvex domains.

Enhances understanding of regularity in the ar-Neumann problem.

Abstract

For a domain $D$ of $\mathbb{C}^n$ which is weakly $q$-pseudoconvex or $q$-pseudoconcave we give a sufficient condition for subelliptic estimates for the $\bar{\partial}$-Neumann problem. The paper extends to domains which are not necessarily pseudoconvex, the results and the techniques of Catlin. MSC: 32D10, 32U05, 32V25