曲线缩短流的延迟抛物正则性
Delayed parabolic regularity for curve shortening flow
AI总结：
本文针对曲线缩短流提出延迟抛物正则性原则，证明从时间$A/π$起一条曲线的正则性可由另一条控制，并以此构造了初始数据仅为$L^1$函数的解。
摘要：
给定两条围成面积为$A$的区域的曲线在曲线缩短流下演化，我们提出一个原则：从时间$A/π$起，其中一条曲线的正则性应可由另一条曲线的正则性控制。我们证明了若干此类结果，并证明在该时间之前不可能有任何估计成立。作为示例应用，我们构造了图示曲线缩短流的解，其初始数据仅为$L^1$函数。
英文摘要：
Given two curves bounding a region of area $A$ that evolve under curve shortening flow, we propose the principle that the regularity of one should be controllable in terms of the regularity of the other, starting from time $A/π$. We prove several results of this form and demonstrate that no estimate can hold before that time. As an example application, we construct solutions to graphical curve shortening flow starting with initial data that is merely an $L^1$ function.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
