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arXiv · 1909.05343

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

Romain Gicquaud
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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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Romain Gicquaud. 2019-09-11. Prescribed non positive scalar curvature on asymptotically hyperbolic manifolds with application to the Lichnerowicz equation. https://arxiv.org/abs/1909.05343

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