Vol. 232, No. 2, 2007

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Complex tangential flows and compactness of the -Neumann operator

Samangi Munasinghe and Emil J. Straube

Vol. 232 (2007), No. 2, 343–354

We provide geometric conditions on the set of boundary points of infinite type of a smooth bounded pseudoconvex domain in n 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 n the 2 results of the second author.

-Neumann operator, compactness, complex tangential flow
Mathematical Subject Classification 2000
Primary: 32W05
Received: 26 July 2006
Revised: 12 January 2007
Accepted: 5 February 2007
Published: 1 October 2007
Samangi Munasinghe
Department of Mathematics
University of Arkansas
Fayetteville, AR 72701
United States
Emil J. Straube
Department of Mathematics
Texas A&M University
College Station, TX 77843
United States