论文标题
带有通用初始数据的平均曲率流量
Mean curvature flow with generic initial data
论文作者
论文摘要
我们表明，$ \ mathbb {r}^{3} $中通用闭合表面的平均曲率流避免了渐近和非球形紧凑型奇点。我们还表明，在$ \ Mathbb {r}^{4} $中，通用封闭的低渗透性高空曲面的平均曲率流是平滑的，直到它在圆点中消失为止。主要的技术成分是长期存在和独特的成分，它是渐近圆锥形或紧凑型孤子的一侧的古代平均曲率流的产生。
We show that the mean curvature flow of generic closed surfaces in $\mathbb{R}^{3}$ avoids asymptotically conical and non-spherical compact singularities. We also show that the mean curvature flow of generic closed low-entropy hypersurfaces in $\mathbb{R}^{4}$ is smooth until it disappears in a round point. The main technical ingredient is a long-time existence and uniqueness result for ancient mean curvature flows that lie on one side of asymptotically conical or compact shrinking solitons.
