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arXiv · 2608.14438

Positive Scalar Curvature and Volume Growth

Bochao Kong·Xingyu Zhu
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Abstract

For a complete Riemannian manifold with nonnegative Ricci curvature, we prove two sharp volume growth order estimates, thereby resolve a conjecture of Gromov in 1986. There first is that a uniform deficit in the volume of unit balls, an analog of positive macroscopic scalar curvature, forces codimension one volume growth, and the second one is that a uniformly positive scalar curvature lower bound forces codimension two growth known as the codimension two volume growth conjecture.

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Bochao Kong, Xingyu Zhu. 2026-08-14. Positive Scalar Curvature and Volume Growth. https://arxiv.org/abs/2608.14438

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