三维流形中嵌入Willmore球面的渐近分析
偏微分方程分析
2017-11-02 v2 微分几何
摘要
在本文中，我们证明，在任意有界Willmore能量假设下，给定维黎曼流形中小直径的嵌入Willmore球面（或更一般地，面积约束下的嵌入Willmore球面）必然集中在的标量曲率的临界点处。这推广了Laurain和Mondino针对小能量嵌入Willmore球面所获得的结果。
引用
@article{arxiv.1710.08732,
title = {Asymptotic Analysis of embedded Willmore spheres in 3-dimensional manifolds},
author = {Chih-Kang Huang},
journal= {arXiv preprint arXiv:1710.08732},
year = {2017}
}
备注
The Theorem 9 in Section 3 of the paper has recently been found by author to be completely wrong. The rest of the results (including the goal of the paper) is then inappropriate and therefore needs to be entirely rewritten