论文标题
$ \ mathbb {r}^{4} $中气泡状椭圆形的分类
Classification of bubble-sheet ovals in $\mathbb{R}^{4}$
论文作者
论文摘要
In this paper, we prove that any bubble-sheet oval for the mean curvature flow in $\mathbb{R}^4$, up to scaling and rigid motion, either is the $\textrm{O}(2)\times \textrm{O}(2)$-symmetric ancient oval constructed by Hershkovits and the fourth author, or belongs to the one-parameter family of $ \ mathbb {z} _2^2 \ times \ textrm {o}（2）$ - 由第三和第四作者构建的对称的古椭圆形。特别是，这似乎是几何流量既不是同一性或自我类似的几何流量的分类结果的第一个实例。
In this paper, we prove that any bubble-sheet oval for the mean curvature flow in $\mathbb{R}^4$, up to scaling and rigid motion, either is the $\textrm{O}(2)\times \textrm{O}(2)$-symmetric ancient oval constructed by Hershkovits and the fourth author, or belongs to the one-parameter family of $\mathbb{Z}_2^2\times \textrm{O}(2)$-symmetric ancient ovals constructed by the third and fourth author. In particular, this seems to be the first instance of a classification result for geometric flows that are neither cohomogeneity-one nor selfsimilar.
