关于极小Heegaard曲面的存在性
微分几何
2025-12-02 v2 几何拓扑
摘要
设为闭定向Riemannian -流形中的强不可约Heegaard曲面。我们证明要么同痕于指标至多为1的极小曲面，要么同痕于围绕非定向极小曲面并附有一个竖直把手的管状邻域的边界。这证实了J. Pitts与J.H. Rubinstein长期以来的猜想。
引用
@article{arxiv.1911.07161,
title = {On the existence of minimal Heegaard surfaces},
author = {Daniel Ketover and Yevgeny Liokumovich and Antoine Song},
journal= {arXiv preprint arXiv:1911.07161},
year = {2025}
}
备注
v1: This preprint supersedes both arXiv:1706.01037 [math.DG] and arXiv:1709.09744 [math.DG]. v2: Main results unchanged, significant improvements in the exposition, several figures added