Lambert, B. orcid.org/0000-0002-5058-3158 and Mäder-Baumdicker, E. (2023) Nonlocal estimates for the Volume Preserving Mean Curvature Flow and applications. Calculus of Variations and Partial Differential Equations, 62. 202. ISSN 0944-2669
Abstract
We obtain estimates on nonlocal quantities appearing in the volume preserving mean curvature flow (VPMCF) in the closed, Euclidean setting. As a result we demonstrate that blowups of finite time type I singularities of VPMCF are ancient solutions to mean curvature flow (MCF), prove that monotonicity methods may always be applied at these finite times and obtain information on the asymptotics of the flow. In the case of type II singularities, asymptotic flows corresponding to ’Hamilton’s rescaling procedures’ are eternal solutions of the MCF.
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Item Type: | Article |
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Copyright, Publisher and Additional Information: | © The Author(s) 2023. 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/. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 02 Aug 2023 15:18 |
Last Modified: | 20 Dec 2023 12:52 |
Published Version: | https://link.springer.com/article/10.1007/s00526-0... |
Status: | Published |
Publisher: | Springer Nature |
Identification Number: | 10.1007/s00526-023-02532-4 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:201799 |
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