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arXiv · 2502.09727

3-Manifolds with positive scalar curvature and bounded geometry

Otis Chodosh·Yi Lai·Kai Xu
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Abstract

We show that a complete contractible 3-manifold with positive scalar curvature and bounded geometry must be $\mathbb R^3$. We also show that an open handlebody of genus larger than 1 does not admit complete metrics with positive scalar curvature and bounded geometry. Our results rely on the maximal weak solution to inverse mean curvature flow due to the third-named author.

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Otis Chodosh, Yi Lai, Kai Xu. 2025-02-13. 3-Manifolds with positive scalar curvature and bounded geometry. https://arxiv.org/abs/2502.09727

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