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Classification of
bubble-sheet ovals in $\mathbb{R}^4$
Beomjun Choi, Panagiota Daskalopoulos, Wenkui Du, Robert Haslhofer and Nataša Šešum |
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Geometry & Topology 29 (2025) 931–1016
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Abstract |
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We prove that any bubble-sheet oval for the mean curvature flow in , up to scaling and rigid motion, either is the -symmetric ancient oval constructed by Haslhofer and Hershkovits, or belongs to the one-parameter family of -symmetric ancient ovals constructed by Du and Haslhofer. In particular, this seems to be the first instance of a classification result for geometric flows that are neither cohomogeneity-one nor selfsimilar. |
Keywords
mean curvature flow, singularities, ancient solutions
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Mathematical Subject Classification
Primary: 53E10
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References |
Publication
Received: 9 March 2023
Revised: 18 March 2024
Accepted: 18 May 2024
Published: 21 April 2025
Proposed: Tobias H Colding
Seconded: Gang Tian, Aaron Naber
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Authors |
| Beomjun Choi | |
| Department of Mathematics POSTECH Gyeongbuk South Korea |
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| Panagiota Daskalopoulos | |
| Department of Mathematics Columbia University New York, NY United States |
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| Wenkui Du | |
| Department of Mathematics Massachusetts Insitute of Technology Cambridge, MA United States |
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| Robert Haslhofer | |
| Department of Mathematics University of Toronto Toronto, ON Canada |
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| Nataša Šešum | |
| Department of Mathematics Rutgers University Piscataway, NJ United States |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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