For a complete manifold M with constant negative curvature, we prove that the rough Laplacian 3R defines topological isomorphisms in the scale of Sobolev spaces Hps (M) of p-forms for all p, 0 < p < n. For the de Rham Laplacian Δ and M = ℍn n, the Poincaré hyperbolic space, this is shown too for 0 ≤ p ≤ n, p 3 ≠ n/2, p 3= (n ± 1)/2.
|Journal||Annals of Global Analysis and Geometry|
|Publication status||Published - 1 Apr 2004|
- Hodge-de Rham Laplacian
- Hyperbolic manifolds
- Riesz transforms
- Rough Laplacian
- Sobolev spaces