沿 Ricci 流的对数 Sobolev 不等式
微分几何
2007-08-29 v4
摘要
我们推导了沿 Ricci 流的对数 Sobolev 不等式，该不等式对时间没有任何限制，仅依赖于通过基本几何数据给出的初始度量，并假设某个第一特征值为正。作为推论，我们获得了沿 Ricci 流且对时间无限制的均匀 Sobolev 不等式。其应用之一是适用于所有时间的均匀 kappa-非坍缩估计。在不假设特征值条件的情况下，我们也获得了针对有界时间的类似结果。这些结果可推广到带有手术的 Ricci 流。
引用
@article{arxiv.0707.2424,
title = {The logarithmic Sobolev inequality along the Ricci flow},
author = {Rugang Ye},
journal= {arXiv preprint arXiv:0707.2424},
year = {2007}
}
备注
One appendix is added. A theorem on the Sobolev inequality along the Ricci flow with surgeries of Perelman is added. Two nonlocal Sobolev inequalities are also added. These results were obtained at the time of the posting of the first version of the paper. They were originally planned as parts of two upcoming papers of the author