The Skew Mean Curvature Flow (SMCF) is a Schrödinger-type geometric flow canonically defined on a co-dimension two submanifold, which generalizes the famous vortex filament equation in fluid dynamics. In this paper, we prove the local existence and uniqueness of general-dimensional SMCF in Euclidean spaces.

中文翻译：

---

偏斜平均曲率流的局部存在唯一性

Skew Mean Curvature Flow (SMCF) 是一种薛定谔型几何流，它规范地定义在同维二子流形上，它概括了流体动力学中著名的涡流丝方程。在本文中，我们证明了一般维 SMCF 在欧几里得空间中的局部存在性和唯一性。