Vol. 10, No. 4, 2017

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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 ${ℝ}^{n+1}$, which is the graph of a real radial function, then the spectrum of the Laplace operator on $M$ is the interval $\left[0,\infty \right)$.

Keywords
Complete surface, Laplace operator, spectrum
Primary: 58J50
Secondary: 58C40