Counterexamples to prescribed scalar curvature in the null case

Yuxiang Li; Yunqing Wu; Jie Zhou

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arXiv · 2610.18432

Counterexamples to prescribed scalar curvature in the null case

Yuxiang Li·Yunqing Wu·Jie Zhou

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Abstract

We construct smooth functions on the flat torus $\mathbb{T}^{n\ge5}$ that change sign and have negative mean but cannot be realized as the scalar curvature of any metric in the given conformal class.

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Yuxiang Li, Yunqing Wu, Jie Zhou. 2026-10-13. Counterexamples to prescribed scalar curvature in the null case. https://arxiv.org/abs/2610.18432

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