锥内演化的星型超曲面的一种逆曲率流类
微分几何
2021-04-21 v2
摘要
给定欧几里得空间（）中的一个光滑凸锥，我们考虑具有边界的严格平均凸超曲面，这些超曲面相对于锥中心是星型的，并且与锥垂直相交。若锥内的这些超曲面按一类逆曲率流演化，则通过在梯度与赫尔德（Hölder）估计推导中利用锥的凸性，我们可以证明该演化对所有时间存在，且演化超曲面随着时间趋于无穷而光滑收敛到一段球面。
引用
@article{arxiv.2104.08884,
title = {A class of inverse curvature flows for star-shaped hypersurfaces evolving in a cone},
author = {Jing Mao and Qiang Tu},
journal= {arXiv preprint arXiv:2104.08884},
year = {2021}
}
备注
17 pages. This paper was finished in January 2019 when the first author visited IST, University of Lisbon. We just put it on arXiv very recently (the status of two references has been updated). Several related works will also be put on arXiv soon. Comments are welcome. Two typos have been corrected in Theorem 1.1