Complex tangential flows and compactness of the ∂-Neumann operator

Samangi Munasinghe and Emil J. Straube

Vol. 232 (2007), No. 2, 343–354

DOI: 10.2140/pjm.2007.232.343

Abstract

We provide geometric conditions on the set of boundary points of infinite type of a smooth bounded pseudoconvex domain in ℂⁿ implying that the ∂-Neumann operator is compact. These conditions are formulated in terms of certain short time flows in suitable complex tangential directions. It is noteworthy that compactness is not established via the known potential theoretic sufficient conditions. Our results generalize to ℂⁿ the ℂ² results of the second author.

Keywords

∂-Neumann operator, compactness, complex tangential flow

Mathematical Subject Classification 2000

Primary: 32W05

Milestones

Received: 26 July 2006

Revised: 12 January 2007

Accepted: 5 February 2007

Published: 1 October 2007