Essential norm estimates for the $\bar{\partial}$-Neumann operator on convex domains and worm domains

TL;DR

This paper provides lower bounds for the essential norm of the ar-Neumann operator specifically on convex and worm domains, advancing understanding of its spectral properties.

Contribution

It introduces new lower estimate techniques for the essential norm of the ar-Neumann operator on complex domains, including worm domains.

Findings

Lower bounds for the essential norm on convex domains

Lower bounds for the essential norm on worm domains

Enhanced spectral analysis of the ar-Neumann operator

Abstract

In the paper we give a lower estimate for the essential norm of the $\bar{\partial}$-Neumann operator on convex domains and worm domains of Diederich and Fornaess.