Abstract
For a complete manifold M with constant negative curvature, weprove that the rough Laplacian Δ R defines topological isomorphisms in the scale of Sobolev spaces H p s(M) ofp-forms for all p, 0 < p< n. For the de Rham LaplacianΔ and M=ℍn, the Poincaréhyperbolic space, this is shown too for 0 ≤p≤n,p≠n/2, p≠ (n± 1)/2.
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Bruna, J., Girbau, J. Mapping Properties of the Laplacian in Sobolev Spaces of Forms on Complete Hyperbolic Manifolds. Annals of Global Analysis and Geometry 25, 151–176 (2004). https://doi.org/10.1023/B:AGAG.0000018554.31037.23
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DOI: https://doi.org/10.1023/B:AGAG.0000018554.31037.23