论文标题
旋转平均曲率流中的不存在的结果，以$ \ mathbb {r}^{4} $
A nonexistence result for rotating mean curvature flows in $\mathbb{R}^{4}$
论文作者
论文摘要
平均曲率流的某些令人担忧的潜在奇异性模型是旋转的古老流动，即$ - \ infty $的切线流量为callinder $ \ mathbb {r}^k \ times s^{n-k} $，并且在$ \ mathbb {r} r}^k $ -factor中旋转。我们注意到，虽然$ \ mathbb {r}^k $ -factor，即圆柱体的轴是独一无二的，这是独一无二的，这是冷淡的微米的基本工作，但切线流的唯一性本身并未提供有关$ \ m athbb {r}^k $ -factor中$ \ sathbb {r}^k $ -factor中旋转的任何信息。在本文中，我们排除在$ \ mathbb {r}^4 $中旋转所有古老的非汇总流中的古老流动。
Some worrisome potential singularity models for the mean curvature flow are rotating ancient flows, i.e. ancient flows whose tangent flow at $-\infty$ is a cylinder $\mathbb{R}^k\times S^{n-k}$ and that are rotating within the $\mathbb{R}^k$-factor. We note that while the $\mathbb{R}^k$-factor, i.e. the axis of the cylinder, is unique by the fundamental work of Colding-Minicozzi, the uniqueness of tangent flows by itself does not provide any information about rotations within the $\mathbb{R}^k$-factor. In the present paper, we rule out rotating ancient flows among all ancient noncollapsed flows in $\mathbb{R}^4$.
