论文标题
水平集的单数集和曲率爆炸速率
Singular set and curvature blow-up rate of the level set flow
论文作者
论文摘要
在某些条件下，例如$ 2 $ - 概念，当且曲率爆炸的速率在单数之前和之后限制了曲率爆破的速率），并且仅当流量缩小到圆点或$ c^{1} $曲线接近该单一点时。从分析上讲，当且仅当它满足该点附近的lojasiewicz不平等时，到达时间是$ c^{2} $。
Under certain conditions such as the $2$-convexity, a singularity of the level set flow is of type I (in the sense that the rate of curvature blow-up is constrained before and after the singular time) if and only if the flow shrinks to either a round point or a $C^{1}$ curve near that singular point. Analytically speaking, the arrival time is $C^{2}$ near a critical point if and only if it satisfies a Lojasiewicz inequality near the point.
