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arXiv · 2404.01660

On open manifolds admitting no complete metric with positive scalar curvature

Yuguang Shi·Jian Wang·Runzhang Wu·Jintian Zhu
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Abstract

In this paper, we investigate the topological obstruction problem for positive scalar curvature and uniformly positive scalar curvature on open manifolds. We present a definition for open Schoen-Yau-Schick manifolds and prove that there is no complete metric with positive scalar curvature on these manifolds. Similarly, we define weak Schoen-Yau-Shick manifolds by analogy, which are expected to admit no complete metrics with uniformly positive scalar curvature.

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Yuguang Shi, Jian Wang, Runzhang Wu, Jintian Zhu. 2024-04-02. On open manifolds admitting no complete metric with positive scalar curvature. https://arxiv.org/abs/2404.01660

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