Vol. 12, No. 1, 2019

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Spectrum of the Kohn Laplacian on the Rossi sphere

Tawfik Abbas, Madelyne M. Brown, Allison Ramasami and Yunus E. Zeytuncu

Vol. 12 (2019), No. 1, 125–140
Abstract

We study the spectrum of the Kohn Laplacian bt on the Rossi example (S3 ,t). In particular we show that 0 is in the essential spectrum of bt, which yields another proof of the global nonembeddability of the Rossi example.

Keywords
Kohn Laplacian, spherical harmonics, global embeddability of CR manifolds
Mathematical Subject Classification 2010
Primary: 32V30
Secondary: 32V05
Supplementary material

Mathematica Code

Milestones
Received: 22 August 2017
Revised: 2 December 2017
Accepted: 30 December 2017
Published: 31 May 2018

Communicated by Stephan Garcia
Authors
Tawfik Abbas
Department of Mathematics
Michigan State University
East Lansing, MI
United States
Madelyne M. Brown
Department of Mathematics
Bucknell University
Lewisburg, PA
United States
Allison Ramasami
Department of Mathematics and Statistics
University of Michigan-Dearborn
Dearborn, MI
United States
Yunus E. Zeytuncu
Department of Mathematics and Statistics
University of Michigan-Dearborn
Dearborn, MI
United States