相互ε-临界点球定理的一个注记(英文)

A Remark on A Sphere Theorem with Mutually s - critical Points

该文利用径向曲率的Toponogov定理,证明了一个球定理:给定Λ>0,存在一正数ε~*=ε~*(Λ),如果n维完备黎曼流形M包含两点p,q,满足p和q相互ε~*-临界点,且d(p,q)~2K_p^(min)≥-Λ,那么M同胚于球S^n。

In this note, using Toponogov theorem for adial curvature, we prove some a sphere theorem for radial curvature.