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arXiv · 2209.04931

Classification of bubble-sheet ovals in $\mathbb{R}^{4}$

Beomjun Choi·Panagiota Daskalopoulos·Wenkui Du·Robert Haslhofer·Natasa Sesum
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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 $\mathbb{Z}_2^2\times \textrm{O}(2)$-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.

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Beomjun Choi, Panagiota Daskalopoulos, Wenkui Du, Robert Haslhofer, Natasa Sesum. 2022-09-11. Classification of bubble-sheet ovals in $\mathbb{R}^{4}$. https://doi.org/10.2140/gt.2025.29.931

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