共形背景下的Cheeger-Gromov收敛
微分几何
2018-08-14 v4
摘要
对于带边界的带点黎曼流形序列 ，若度量 与 共形，即 ，则序列 为其共形卫星。假设流形 具有一致有界几何，我们证明只要共形因子 是某个适当椭圆算子的主特征函数，这两个序列都有光滑的Cheeger-Gromov收敛子列。我们结果的一部分是带边界流形的Cheeger-Gromov紧性。我们使用了最近建立的'flatzoomer'方法中的经典椭圆估计与不等式的稳定版本。
引用
@article{arxiv.1512.07651,
title = {Cheeger-Gromov convergence in a conformal setting},
author = {Boris Botvinnik and Olaf Müller},
journal= {arXiv preprint arXiv:1512.07651},
year = {2018}
}
备注
25 pages. The authors discovered a mistake in the paper. In particular, the claim of Theorem B does not hold, however Theorem A still true, and, by insistence of the first author, Theorem A will be published by the second author in a separate paper