论文标题
稳定技术适用于曲线缩短流量$ \ mathbb {r}^3 $
Stabilization technique applied to curve shortening flow in $\mathbb{R}^3$
论文作者
论文摘要
我们将1960年代T. Zelenyak开发的稳定技术应用于抛物线方程，在$ \ r^3 $中的曲线缩短流程上，并得出了几种新的单调性公式。所有这些都共享一个主要特征：“能量”项对位置向量和平面正交与切线矢量之间的角度的依赖性。第一个公式介绍了单位球上曲线的投影，并计算其长度的派生。第二个公式是G. huisken的经典公式的概括，而第三个公式是单调性公式的概括，该公式的概括为作者先前用于平面曲线的对数项。
We apply the stabilization technique, developed by T. Zelenyak in 1960s for parabolic equations, on curve shortening flow in $\R^3$, and derive several new monotonicity formulas. All of them share one main feature: the dependence of the "energy" term on the angle between the position vector and the plane orthogonal to the tangent vector. The first formula deals with the projection of the curve on the unit sphere, and computes the derivative of its length. The second formula is the generalization of the classical formula of G. Huisken, while the third one is the generalization of the monotonicity formula with logarithmic terms previously derived by the author for plane curves.
