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arXiv · 2407.05574

Complete Riemannian 4-manifolds with uniformly positive scalar curvature

Otis Chodosh·Davi Maximo·Anubhav Mukherjee
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Abstract

We obtain topological obstructions to the existence of a complete Riemannian metric with uniformly positive scalar curvature on certain (non-compact) $4$-manifolds. In particular, such a metric on the interior of a compact contractible $4$-manifold uniquely distinguishes the standard $4$-ball up to diffeomorphism among Mazur manifolds and up to homeomorphism in general. We additionally show there exist uncountably many exotic $\mathbb{R}^4$'s that do not admit such a metric and that any (non-compact) tame $4$-manifold has a smooth structure that does not admit such a metric.

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Otis Chodosh, Davi Maximo, Anubhav Mukherjee. 2024-07-08. Complete Riemannian 4-manifolds with uniformly positive scalar curvature. https://arxiv.org/abs/2407.05574

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