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Wave and Klein-Gordon equations on hyperbolic spaces

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arxiv 1104.0177 v2 pith:G5SKNHLC submitted 2011-04-01 math.AP math.CA

Jean-Philippe Anker (MAPMO) , Vittoria Pierfelice (MAPMO) This is my paper · ORCID
classification math.APmath.CA
keywords equationdeltahyperbolicspaceswaveadmissibleanalysisapplication
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abstract

We consider the Klein--Gordon equation associated with the Laplace--Beltrami operator $\Delta$ on real hyperbolic spaces of dimension $n\!\ge\!2$; as $\Delta$ has a spectral gap, the wave equation is a particular case of our study. After a careful kernel analysis, we obtain dispersive and Strichartz estimates for a large family of admissible couples. As an application, we prove global well--posedness results for the corresponding semilinear equation with low regularity data.

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    Dark energy and dark matter are proposed to be, respectively, the vacuum and ground-state eigenvalues of a density operator from canonical quantum gravity, yielding accelerating Friedmann solutions under assumed low t...

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