无重点的曲线也称为简单曲线，无重点的闭曲线称为简单闭曲线。
设B是一个复的向量空间，它是由环链在平环上的简单闭曲线生成。
Let B be a complex vector space generated by some simple closed curves in the annulus.
本文给出了关于全挠率的一个著名定理：“球面闭曲线的全挠率为零”一个新的简单证法，并且给出了这个定理的两个推广定理。
A new and simple proving method on the famous theorem of total torsion, "the total torsion of closed spherical curve is zero", and two generalized theorems for the. theorem are presented in the paper.
由此结合尺度论证法得到平面光滑简单闭凸曲线在上述曲线流下的渐近性态。
Moreover, by combining the estimate with the rescaling argument, obtains the asymptotic behaviour of the flow with initial simple closed convex curves.
应用推荐