Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.12479 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- J. Rosenberg's $\mathbb{S}^1$-stability conjecture states that a closed oriented manifold $X$ admits a positive scalar curvature metric iff $X\times \mathbb{S}^1$ admits a positive scalar curvature metric $h$. As pointed out by J. Rosenberg and others, there are known counterexamples in dimension four. We prove this conjecture whenever $h$ satisfies a geometric bound which measures the discrepancy between $\partial_θ\in T\mathbb{S}^1$ and the normal vector field to $X\times \{P\}$, for a fixed $P\in \mathbb{S}^1.$