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arXiv · 2512.13528

Scalar Curvature in Dimension 4

Jialong Deng
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Abstract

We prove that every locally conformally flat metric on a closed, oriented hyperbolic 4-manifold with scalar curvature bounded below by -12 satisfies Schoen's conjecture. We also classify all closed Riemannian 4-manifolds of positive scalar curvature that arise as total spaces of fibre bundles. For a closed locally conformally flat 4-manifold with scalar curvature zero and nontrivial second homotopy group, we show that its universal Riemannian cover is homothetic to the standard product of the hyperbolic plane and the round 2-sphere. This affirmatively answers a question of N. H. Noronha.

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Jialong Deng. 2025-12-15. Scalar Curvature in Dimension 4. https://arxiv.org/abs/2512.13528

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