Sectoriality of the Laplacian on Asymptotically Hyperbolic Spaces

Abstract

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 Hölder spaces. As an application, the machinery of analytic semigroups then applies to yield well-posedness results for parabolic evolution equations in these spaces.

This manuscript is no longer intended for publication and has been replaced by our new work at arXiv:2210.15886 which corrects and extends these results