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arXiv · 2502.14216

Interior control for surfaces with positive scalar curvature and its application

Shuli Chen·Jianchun Chu·Jintian Zhu
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Abstract

Let $M^{n}$, $n\in\{3,4,5\}$, be a closed aspherical $n$-manifold and $S\subset M$ a subset consisting of disjoint incompressible embedded closed aspherical submanifolds (possibly with different dimensions). When $n =3,4$, we show that $M\setminus S$ cannot admit any complete metric with positive scalar curvature. When $n=5$, we obtain the same result when $S$ contains a submanifold of codimension 1 or 2. The key ingredient is a new interior control for the extrinsic diameter of surfaces with positive scalar curvature.

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Shuli Chen, Jianchun Chu, Jintian Zhu. 2025-02-20. Interior control for surfaces with positive scalar curvature and its application. https://arxiv.org/abs/2502.14216

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