English

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 L2L^2 norm has a subsequence which converges to some flat metric on the three-torus in the sense of Dong-Song.

Keywords

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