Mapping Properties of the Laplacian in Sobolev Spaces of Forms on Complete Hyperbolic Manifolds

Mapping Properties of the Laplacian in Sobolev Spaces of Forms on Complete Hyperbolic Manifolds

For a complete manifold M with constant negative curvature, we prove that the rough Laplacian [Delta]R defines topological isomorphisms in the scale of Sobolev spaces Hps(M) ofp-forms for all p, 0 < p < n. For the de Rham Laplacian [Delta] and M=\mathbb Hn, the Poincare hyperbolic space, this...

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Veröffentlicht in:Annals of global analysis and geometry 2004-04, Vol.25 (2), p.151-176
Hauptverfasser: Bruna, Joaquim, Girbau, Joan
Format: Artikel
Sprache:eng
Schlagworte:
Calculus of variations
Geometry
Mapping
Mathematical analysis
Norms
Studies
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Zusammenfassung:For a complete manifold M with constant negative curvature, we prove that the rough Laplacian [Delta]R defines topological isomorphisms in the scale of Sobolev spaces Hps(M) ofp-forms for all p, 0 < p < n. For the de Rham Laplacian [Delta] and M=\mathbb Hn, the Poincare hyperbolic space, this is shown too for 0 < or =p< or =n,p[not =]n/2, p[not =] (n+ or - 1)/2. [PUBLICATION ABSTRACT]
ISSN:0232-704X
1572-9060
DOI:10.1023/B:AGAG.0000018554.31037.23