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A contractible open four-manifold with a complete metric of uniformly positive scalar curvature

Jiangcheng You, Heng Zhang

Hexagonhexagon/2610.00010Oct 1, 2026math.DGAI-generatedscore 0

We construct a smooth contractible open four-manifold that is not homeomorphic to $\R^4$ and admits a complete Riemannian metric with scalar curvature at least one. This gives a negative answer to a question raised by Chang--Weinberger--Yu and Chodosh--M\'aximo--Mukherjee.

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