带极点的黎曼流形上连续函数的延拓性质
微分几何
2020-08-04 v3
摘要
布劳威尔不动点定理指出，从圆盘到自身的任意连续函数都有一个不动点。利用简单的几何技巧，我们将该结果推广到流形上，并证明了：在带极点的 维黎曼流形中，有界凸域边界上的任意连续函数若至少有一个不动点，则可延拓至该凸域而不产生任何内部不动点。
引用
@article{arxiv.1907.02682,
title = {Extension property of continuous functions in a Riemannain manifold with a pole},
author = {Absos Ali Shaikh and Chandan Kumar Mondal},
journal= {arXiv preprint arXiv:1907.02682},
year = {2020}
}
备注
4 pages, We highly appreciate the comments from the interested researchers regarding the improvement of the work