Stability for a class of three-tori with small negative scalar curvature
Differential Geometry
2024-05-15 v2
Abstract
We define a flexible class of Riemmanian metrics on the three-torus. Then, using Stern's inequality relating scalar curvature to harmonic one-forms, we show that any sequence of metrics in this family whose negative part of the scalar curvature tends to zero in norm has a subsequence which converges to some flat metric on the three-torus in the sense of Dong-Song.
Cite
@article{arxiv.2404.12795,
title = {Stability for a class of three-tori with small negative scalar curvature},
author = {Edward Bryden and Lizhi Chen},
journal= {arXiv preprint arXiv:2404.12795},
year = {2024}
}
Comments
In the second version, the abstract is updated; some typos are corrected