至少四维度下负曲率Einstein度量的有效稳定性
微分几何
2025-12-30 v2
摘要
我们证明，如果一个维度至少为四的闭合流形 admits a negatively curved metric that is almost Einstein in a suitable sense, then it admits a genuine Einstein metric of negative sectional curvature. Importantly, the pinching constant measuring the almost-Einstein condition neither depends on an upper bound for the diameter or volume, nor on a lower bound for the injectivity radius.
关键词
引用
@article{arxiv.2502.16692,
title = {Effective stability of negatively curved Einstein metrics in dimensions at least $4$},
author = {Frieder Jäckel},
journal= {arXiv preprint arXiv:2502.16692},
year = {2025}
}
备注
19 pages. Version 2 removes the restriction on the dimension