维数 $n\geq 3$ 时 $\mathbb{S}^{n-1}$ 共形群的稳定性估计
微分几何
2021-03-16 v3 偏微分方程分析
摘要
本文旨在给出当 时 的 M"obius 变换类的一个定量稳定性结果。主要估计具有局部性质，并断言对于一个先验接近于 M"obius 变换的 Lipschitz 映射，一种平均共形等周型亏控控制了该映射与某个特定 M"obius 映射的偏差（在平均意义下）。文中还讨论了该结果的最优性及其与特殊正交群几何刚性的联系。
引用
@article{arxiv.1910.01862,
title = {Stability estimates for the conformal group of $\mathbb{S}^{n-1}$ in dimension $n\geq 3$},
author = {Stephan Luckhaus and Konstantinos Zemas},
journal= {arXiv preprint arXiv:1910.01862},
year = {2021}
}
备注
This paper has been withdrawn by the authors because the results are now contained (in a reorganized and improved form) in a new paper (arXiv:2101.03846). A mistake in the last part of Lemma 3.2. (ii) (making Theorems 3.5. and 5.4. invalid) has been corrected in the new paper (see Lemma 5.3 and Subsections 5.2 and 5.3 therein)