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arXiv · 2302.02435

Prescribing scalar curvatures: on the negative Yamabe case

Martin Mayer·Chaona Zhu
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Abstract

The problem of prescribing conformally the scalar curvature on a closed Riemannian manifold of negative Yamabe invariant is always solvable, when the function $K$ to be prescribed is strictly negative, while sufficient and necessary conditions are known for $K\leq 0$. For sign changing $K$ Rauzy showed solvability, if $K$ is not too positive. We revisit this problem in a different variational context, thereby recovering and quantifying the principle existence result of Rauzy and show under additional assumptions, that for a sign changing $K$ solutions to the conformally prescribed scalar curvature problem, while existing, are not unique.

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Martin Mayer, Chaona Zhu. 2023-02-05. Prescribing scalar curvatures: on the negative Yamabe case. https://doi.org/10.1142/s0219199726500586

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