带边流形上在Yamabe型流下的标量平坦度量的收敛性
微分几何
2015-08-07 v3 偏微分方程分析
摘要
我们研究了一个维数大于2的带边紧致黎曼流形上的共形流。在维数不超过7时，以及在流形是旋量或满足一般条件时任意维数下，建立了收敛到边界上具有常平均曲率的标量平坦度量。
引用
@article{arxiv.1206.1184,
title = {Convergence of scalar-flat metrics on manifolds with boundary under a Yamabe-type flow},
author = {Sergio Almaraz},
journal= {arXiv preprint arXiv:1206.1184},
year = {2015}
}
备注
Title slightly changed. Introduction improved and changed to include the recent results (arXiv:1407.0673) on Conjecture 1.5. Appendix C removed and published as a separate paper (arXiv:1508.01058). Although Appendix B was shortened for publication, this arxiv version remains complete and unchanged. Some typos corrected. 71 pages