Liouville 正则 Jordan 曲线
Liouville regular Jordan curves
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中文总结 AI 辅助
本文研究 Liouville 正则 Jordan 曲线类，通过变分条件和共形映射下径向尾部长度消失的准则，证明此类曲线存在，并由此得出每个相似类中都有内接矩形。
中文摘要 AI 辅助
我们研究了 Liouville 正则 Jordan 曲线类，该类在我们之前的论文中以“允许连续 Legendrian 提升的 Jordan 曲线”这一表述引入。我们证明，若一条 Jordan 曲线在每个点的邻域内满足某种变分条件，则它属于此类。我们还证明，若共形映射下径向尾部的像具有一致消失的长度，则 Jordan 区域的边界是 Liouville 正则的。结合我们之前的结果，这些准则蕴含了在每个给定的相似类中都存在内接矩形。
英文摘要
We investigate the class of Liouville regular Jordan curves, which was introduced in our previous paper under the phrase "Jordan curves that admit continuous Legendrian lifts". We prove that a Jordan curve satisfying certain variation condition in a neighborhood of each point is in this class. We also prove that the boundary of a Jordan domain is Liouville regular if the images of the radial tails under a conformal mapping have uniformly vanishing length. Together with our previous result, these criteria imply the existence of an inscribed rectangle in every prescribed similarity class.
发表机构
- Kyoto University（京都大学）
- The University of Tokyo（东京大学）
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