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Classification of bubble-sheet ovals in $\mathbb{R}^{4}$ (2209.04931v3)
Published 11 Sep 2022 in math.DG and math.AP
Abstract: 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 $\mathbb{Z}_22\times \textrm{O}(2)$-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.