Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2401.02136 |
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Sommario:
- In this article, we find sufficient conditions on an open Riemannian manifold so that a Weyl criterion holds for the $L^p$-spectrum of the Laplacian on $k$-forms, and also prove the decomposition of the $L^p$-spectrum depending on the order of the forms. We then show that the resolvent set of an operator such as the Laplacian on $L^p$ lies outside a parabola whenever the volume of the manifold has an exponential volume growth rate, removing the requirement on the manifold to be of bounded geometry. We conclude by providing a detailed description of the $L^p$ spectrum of the Laplacian on $k$-forms over hyperbolic space.