Ricci流下测地球体积增长的上界
微分几何
2011-10-11 v2 偏微分方程分析
摘要
我们证明了Ricci流的一个所谓的κ非膨胀性质，该性质在标量曲率有上界的条件下，给出了测地球体积与欧氏球体积之比的的上界。该结果可视为Perelman关于Ricci流的κ非坍缩性质的对立陈述。这两个结果共同推导出Ricci流在不假设Ricci曲率下界时的体积加倍性质。
引用
@article{arxiv.1107.4262,
title = {Bounds on volume growth of geodesic balls under Ricci flow},
author = {Qi S. Zhang},
journal= {arXiv preprint arXiv:1107.4262},
year = {2011}
}
备注
One reference on related result [CW2] added. A typo at last line of p3 corrected. The last coefficient p(t) in the line should be in front of \Delta u only