重数一极小极大极小超曲面的 Morse 指标
微分几何
2019-01-11 v2 偏微分方程分析
摘要
本文证明，一个重数为一、光滑的极小极大极小超曲面的 Morse 指标通常等于构造中所用族所检测的同调类的维数。这证实了作者提出的（旨在为面积泛函发展 Morse 理论）研究纲领（\cite{marques-icm}, \cite{marques-neves-cycles}, \cite{marques-neves-index}, \cite{neves-icm}）的一部分。
引用
@article{arxiv.1803.04273,
title = {Morse index of multiplicity one min-max minimal hypersurfaces},
author = {Fernando C. Marques and André Neves},
journal= {arXiv preprint arXiv:1803.04273},
year = {2019}
}
备注
53 pages. We have added an Addendum to reflect the solution by X. Zhou of our Multiplicity One Conjecture 1.2. We have extended our Main Theorem 1.3 to obtain, in light of Zhou's paper, the precise characterization of the Morse index of min-max minimal hypersurfaces for generic metrics. This finishes the Morse-theoretic program proposed by the authors for the area functional (Theorem 8.4)