Morse Index Bound for Minimal Two Spheres

被引：0
作者：
Yuchin Sun
机构：
[1] UC Santa Cruz,
来源：
The Journal of Geometric Analysis | 2022年 / 32卷
关键词：
Morse index; Min–max; Minimal sphere; Harmonic map; 53A10;
D O I：
暂无
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摘要：
Given a closed manifold of dimension at least three, with non-trivial homotopy group π3(M)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi _3(M)$$\end{document} and a generic metric, we prove that there is a finite collection of harmonic spheres with Morse index bounded by one, with sum of their energies realizing a geometric invariant width.
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