代数曲线的利普希茨嵌入
Lipschitz embeddings of algebraic curves
AI总结：
研究实代数曲线利普希茨分类，证明其内部与\(\mathbb{R}^3\)中具LNE连通分量的外部分类等价，找到实仿射代数曲线的LNE模型，还指出复范畴不成立此结论。
AI中文摘要：
我们证明了实代数曲线的内部利普希茨分类等同于在\(\mathbb{R}^3\)中具有LNE连通分量的实代数曲线的外部利普希茨分类。此外，对于每一条实仿射代数曲线，我们找到了与之实双有理的LNE模型。最后，我们表明该结论在复范畴中不成立。
英文摘要：
We show that inner Lipschitz classification of real algebraic curves is equivalent to outer Lipschitz classification in $\mathbb{R}^3$ of real algebraic curves with LNE connected components. Moreover, for every real affine algebraic curve we find its LNE model which is real birational to it. Lastly, we show that this claim does not hold in the complex category.
