距Jordan曲线的常距集
Sets of constant distance from a Jordan curve
摘要：
我们研究了平面Jordan曲线$Γ$的符号距离函数的$ε$ -水平集，并问$Γ$的什么性质保证了$ε$ -水平集是Jordan曲线，或均匀拟圆，或均匀弦弧曲线，对于所有足够小的$ε$ .利用尺度不变参数给出了测量子弧与弦的局部偏差的充分条件。给出的弦条件是严格的。
英文摘要：
We study the $ε$-level sets of the signed distance function to a planar Jordan curve $Γ$, and ask what properties of $Γ$ ensure that the $ε$-level sets are Jordan curves, or uniform quasicircles, or uniform chord-arc curves for all sufficiently small $ε$. Sufficient conditions are given in term of a scaled invariant parameter for measuring the local deviation of subarcs from their chords. The chordal conditions given are sharp.
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