Volume comparison theorem with respect to sigma-2 curvature
Differential Geometry
2023-12-12 v2
Abstract
In this paper, we investigate the volume comparison theorem related to -curvature. In particular, we show that volume comparison theorem with respect to -curvature holds for metrics close to strictly stable positive Einstein metrics. By applying similar techniques, we derive the local rigidity theorem for strictly stable Ricci flat manifolds with respect to -curvature, which shows it admits no metric with positive -curvature near strictly stable Ricci-flat metrics.
Cite
@article{arxiv.2111.09532,
title = {Volume comparison theorem with respect to sigma-2 curvature},
author = {Jiaqi Chen and Yi Fang and Yan He and Jingyang Zhong},
journal= {arXiv preprint arXiv:2111.09532},
year = {2023}
}
Comments
18 pages