THE LAPLACE SPECTRUM ON CONFORMALLY COMPACT MANIFOLDS

Journal article, 2024

We consider the spectrum of the Laplace operator acting on L-p over a conformally compact manifold for 1 < p < infinity. We prove that for p not equal 2 this spectrum always contains an open region of the complex plane. We further show that the spectrum is contained within a certain parabolic region of the complex plane. These regions depend on the value of p, the dimension of the manifold, and the values of the sectional curvatures approaching the boundary.