具有标量曲率下界的三维流形的底谱
微分几何
2024-06-05 v1 偏微分方程分析
摘要
Cheng的一个经典结果表明，具有固定维数和里奇曲率下界的完备流形的底谱在相应的双曲空间上达到最大值。本文在必要的拓扑假设下，建立了具有标量曲率下界的三维完备流形的类似结果。还讨论了刚性，并得到了具有最大底谱的此类流形的分裂定理。
引用
@article{arxiv.2406.02516,
title = {Bottom spectrum of three-dimensional manifolds with scalar curvature lower bound},
author = {Ovidiu Munteanu and Jiaping Wang},
journal= {arXiv preprint arXiv:2406.02516},
year = {2024}
}
备注
The sharp spectral bound was initially included in arXiv:2201.05595 by the same authors; now it is part of this separate submission, which also covers rigidity results. Final version, to appear in Journal of Functional Analysis. 30 pages. arXiv:2201.05595 has been updated to reflect its new content