The Laplace spectrum on conformally compact manifolds

Charalambous, Nelia; Rowlett, Julie

doi:10.1090/tran/9107

The Laplace spectrum on conformally compact manifolds
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by Nelia Charalambous and Julie Rowlett;

Trans. Amer. Math. Soc. 377 (2024), 3373-3395

DOI: https://doi.org/10.1090/tran/9107

Published electronically: February 26, 2024

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Abstract:

We consider the spectrum of the Laplace operator acting on $\mathcal {L}^p$ over a conformally compact manifold for $1 \leq p \leq \infty$. We prove that for $p \neq 2$ 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.

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The Laplace spectrum on conformally compact manifolds
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Abstract: