三维曲率有下界区域的 Ricci 流
微分几何
2017-05-30 v2
摘要
我们考虑三维无边流形上具有有界曲率的 Ricci 流的光滑完备解。假设在零时刻半径为 1 的开球其曲率有下界 -1，那么我们证明了估计式，表明该球内紧包含的子区域将在一个短暂但明确定义的时间区间内被 Ricci 流平滑化。我们获得的估计仅依赖于球的初始体积以及紧区域到初始球边界的距离。利用缩放论证可得半径为 r 的球的这些估计的推广形式。
引用
@article{arxiv.1407.1251,
title = {Ricci Flow of regions with curvature bounded below in dimension three},
author = {Miles Simon},
journal= {arXiv preprint arXiv:1407.1251},
year = {2017}
}
备注
Journal version (2017, 'Journal of Geometric Analysis'). There are changes to notation. I included two new lemmata, Lemma 3.3 and 3.4, the content of which was previously in the proof of Theorem 1.6. New Remark, Remark 4.2, explains in more detail, how the constants appearing in the proof of Theorem 1.6 are chosen