Vol. 10, No. 4, 2017

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ISSN: 1944-4184 (e-only)
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Spectrum of the Laplacian on graphs of radial functions

Rodrigo Matos and Fabio Montenegro

Vol. 10 (2017), No. 4, 677–690
Abstract

We prove that if M is a complete, noncompact hypersurface in n+1, which is the graph of a real radial function, then the spectrum of the Laplace operator on M is the interval [0,).

Keywords
Complete surface, Laplace operator, spectrum
Mathematical Subject Classification 2010
Primary: 58J50
Secondary: 58C40
Milestones
Received: 22 February 2016
Revised: 26 June 2016
Accepted: 11 July 2016
Published: 7 March 2017

Communicated by Martin J. Bohner
Authors
Rodrigo Matos
Department of Mathematics
Michigan State University
East Lansing, MI 48824
United States
Fabio Montenegro
Departamento de Matemática
Universidade Federal do Ceará (UFC)
Av. Humberto Monte, s/n
Campus do Pici, Bloco 914
60455-760 Fortaleza-
Brazil