论文标题
全球和局部偏斜曲率流的理论
Global and local theory of skew mean curvature flows
论文作者
论文摘要
在本文中，我们研究了平均曲率流量。结果是三倍。首先，我们证明了解决方案的全球规律性，这些解决方案具有初始数据，这些数据是Sobolev空间中平面的小扰动。其次，我们证明了修改的散射和小数据的波算子的存在，这完全决定了渐近状态的集合。第三，我们研究了任意大数据的凯奇问题。
In this paper, we study the skew mean curvature flow. The results are threefold. First, we prove the global regularity of solutions with initial data which are small perturbations of planes in Sobolev spaces. Second, we prove the modified scattering and the existence of wave operators for small data, which completely determines the set of asymptotic states. Third, we study the Cauchy problem for arbitrary large data.
