关于谱意义下非负曲率的闭曲面
微分几何
2023-03-20 v2
摘要
我们研究满足谱条件的闭可定向曲面，其中为正常数，为高斯曲率。该条件在正数量曲率的3-流形中稳定极小曲面上自然出现。我们给出了此类曲面的等周不等式、面积增长定理和直径估计。这些不等式的成立依赖于的某些界。对应于正上解，共形度量具有逐点非负曲率。利用新度量的几何，我们证明了关于主谱条件的Hölder预紧性和几乎刚性结果。
引用
@article{arxiv.2211.11715,
title = {On closed surfaces with nonnegative curvature in the spectral sense},
author = {Kai Xu},
journal= {arXiv preprint arXiv:2211.11715},
year = {2023}
}
备注
v2 updates: the article is largely re-written. Two main theorems are added. Section 2 is organized in a better way. Some original proofs in section 4 are simplified. The example in appendix B is replaced. Introduction and abstract are modified accordingly. The title is changed in order to avoid formulas. 26 pages. Comments are welcomed