Global Regularity of Skew Mean Curvature Flow for Small Data in d ≥ 4 Dimensions
Global Regularity of Skew Mean Curvature Flow for Small Data in d ≥ 4 Dimensions
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DOI：
10.1093/imrn/rnad104
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发表时间：
2022-09
影响因子：
1
通讯作者：
Jiaxi Huang;Ze Li;D. Tataru
中科院分区：
文献类型：
--
作者：
Jiaxi Huang;Ze Li;D. Tataru
斜平均曲率流是浸入$\mathbb {R}^{d+2}$中的$d$维流形的演化方程，它以与其平均曲率成正比的速度沿副法线方向沿着运动.在这篇文章中，我们证明了小数据的整体正则性在低正则性Sobolev空间的斜平均曲率流的尺寸$d\geq 4$。这推广了[7]中的局部适定性结果。
The skew mean curvature flow is an evolution equation for a $d$ dimensional manifold immersed into $\mathbb {R}^{d+2}$, and which moves along the binormal direction with a speed proportional to its mean curvature. In this article, we prove small data global regularity in low-regularity Sobolev spaces for the skew mean curvature flow in dimensions $d\geq 4$. This extends the local well-posedness result in [7].