Prescribed non positive scalar curvature on asymptotically hyperbolic manifolds with application to the Lichnerowicz equation

We study the prescribed scalar curvature problem, namely finding which function can be obtained as the scalar curvature of a metric in a given conformal class. We deal with the case of asymptotically hyperbolic manifolds and restrict ourselves to non positive prescribed scalar curvature. Following e...

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Bibliographic Details
Published in:arXiv.org 2019-09
Main Author: Gicquaud, Romain
Format: Article
Language:English
Subjects:
Asymptotic properties
Curvature
Manifolds
Online Access:Get full text
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Summary:We study the prescribed scalar curvature problem, namely finding which function can be obtained as the scalar curvature of a metric in a given conformal class. We deal with the case of asymptotically hyperbolic manifolds and restrict ourselves to non positive prescribed scalar curvature. Following earlier results, we obtain a necessary and sufficient condition on the zero set of the prescribed scalar curvature so that the problem admits a (unique) solution.
ISSN:2331-8422