Cohomologie L^p et formes harmoniques

2010/06/03 by Noël Lohoué, Lohoué, Noël
Mathematics · #Advanced Harmonic Analysis Research #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Spectral Theory (math.SP) #math.DG #math.SP

paper · pdf · doi:10.48550/arxiv.1006.0666

9 pages

arxiv created 2010/06/03 · openalex publication_date 2010/06/03 · arxiv updated 2010/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that a if a Riemannian manifold admits a universal cover with bounded geometry and if 0 does not belong to the spectrum or is an isolated point in the spectrum of the Laplacian on ℓ-forms, then there exists 1<p<2 such that for all p<r<p^′ the Hodge - de Rham decomposition for L^r-forms holds (p^′ denotes the conjugate of p).

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