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

2019/09/11 by Romain Gicquaud, Gicquaud, Romain
Mathematics · #53A30 (Primary) #53C20 #58J05 (Secondary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1909.05343

openalex publication_date 2019/09/11 · openalex created_date 2019/09/19 · openalex updated_date 2026/07/28

Abstract

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.

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