The Laplace spectrum on conformally compact manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913510725779456 |
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| author | Charalambous, Nelia Rowlett, Julie |
| author_facet | Charalambous, Nelia Rowlett, Julie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_09291 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Laplace spectrum on conformally compact manifolds Charalambous, Nelia Rowlett, Julie Spectral Theory 58c40, 58j05, 58j35, 58j50 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. |
| title | The Laplace spectrum on conformally compact manifolds |
| topic | Spectral Theory 58c40, 58j05, 58j35, 58j50 |
| url | https://arxiv.org/abs/2306.09291 |