论文标题
摩尔斯指数绑定到最小两个球
Morse Index Bound for Minimal Two Spheres
论文作者
论文摘要
鉴于尺寸至少三个封闭的歧管，没有琐碎的同型π_3（m）和一个通用指标，我们证明存在有限的谐波球，带有摩尔斯索引索引绑定的谐波球，其能量总和实现了几何不变宽度。
Given a closed manifold of dimension at least three, with non trivial homotopy group π_3(M) and a generic metric, we prove that there is a finite collection of harmonic spheres with Morse index bound one, with sum of their energies realizes a geometric invariant width.
