Mapping properties of the Laplacian in Sobolev spaces of forms on complete hyperbolic manifolds

Joaquim Bruna, Joan Girbau

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)151-176
JournalAnnals of Global Analysis and Geometry
Volume25
DOIs
Publication statusPublished - 1 Apr 2004

Keywords

  • Hodge-de Rham Laplacian
  • Hyperbolic manifolds
  • Riesz transforms
  • Rough Laplacian
  • Sobolev spaces

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