Pinched ancient solutions to the high codimension mean curvature flow
| dc.contributor.author | Lynch, S | |
| dc.contributor.author | Nguyen, HT | |
| dc.date.accessioned | 2021-06-03T11:02:49Z | |
| dc.date.available | 2021-06-03T11:02:49Z | |
| dc.date.issued | 2021-02-01 | |
| dc.identifier.citation | Lynch, Stephen, and Huy The Nguyen. "Pinched Ancient Solutions To The High Codimension Mean Curvature Flow". Calculus Of Variations And Partial Differential Equations, vol 60, no. 1, 2021. Springer Science And Business Media LLC, doi:10.1007/s00526-020-01888-1. Accessed 3 June 2021. | en_US |
| dc.identifier.issn | 0944-2669 | |
| dc.identifier.uri | https://qmro.qmul.ac.uk/xmlui/handle/123456789/72271 | |
| dc.description.abstract | We study solutions of high codimension mean curvature flow defined for all negative times, usually referred to as ancient solutions. We show that any compact ancient solution whose second fundamental form satisfies a certain natural pinching condition must be a family of shrinking spheres. Andrews and Baker (J Differ Geom 85(3):357–395, 2010) have shown that initial submanifolds satisfying this pinching condition, which generalises the notion of convexity, converge to round points under the flow. As an application, we use our result to simplify their proof. | en_US |
| dc.publisher | Springer | en_US |
| dc.relation.ispartof | Calculus of Variations and Partial Differential Equations | |
| dc.rights | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. | |
| dc.rights | Attribution 3.0 United States | * |
| dc.rights.uri | http://creativecommons.org/licenses/by/3.0/us/ | * |
| dc.title | Pinched ancient solutions to the high codimension mean curvature flow | en_US |
| dc.type | Article | en_US |
| dc.rights.holder | © 2021, The Author(s) | |
| dc.identifier.doi | 10.1007/s00526-020-01888-1 | |
| pubs.issue | 1 | en_US |
| pubs.notes | Not known | en_US |
| pubs.publication-status | Published | en_US |
| pubs.volume | 60 | en_US |
| rioxxterms.funder | Default funder | en_US |
| rioxxterms.identifier.project | Default project | en_US |
| qmul.funder | Advances in Mean Curvature Flow: Theory and Applications::Engineering and Physical Sciences Research Council | en_US |
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