Sectoriality of the Laplacian on Asymptotically Hyperbolic Spaces
Analysis of PDEs
2023-04-20 v2 Differential Geometry
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 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.
Keywords
Cite
@article{arxiv.2109.00096,
title = {Sectoriality of the Laplacian on Asymptotically Hyperbolic Spaces},
author = {Eric Bahuaud and Christine Guenther and James Isenberg},
journal= {arXiv preprint arXiv:2109.00096},
year = {2023}
}
Comments
This manuscript is no longer intended for publication and has been replaced by our new work at arXiv:2210.15886 which corrects and extends these results