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Sectoriality of the Laplacian on Asymptotically Hyperbolic Spaces

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arxiv 2109.00096 v2 pith:QZ4BVKSH submitted 2021-08-31 math.AP math.DG

Sectoriality of the Laplacian on Asymptotically Hyperbolic Spaces

Eric Bahuaud , Christine Guenther , James Isenberg This is my paper
classification math.AP math.DG
keywords laplacianspacesasymptoticallyhyperbolicanalyticapplicationappliesequations
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We prove that both the Laplacian on functions, and the Lichnerowicz Laplacian on symmetric 2-tensors with respect to asymptotically hyperbolic metrics, are sectorial maps in weighted H\"older spaces. As an application, the machinery of analytic semigroups then applies to yield well-posedness results for parabolic evolution equations in these spaces.

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