Evans, CG, Lambert, B orcid.org/0000-0002-5058-3158 and Wood, A (2022) Lagrangian Mean Curvature Flow with Boundary. Calculus of Variations and Partial Differential Equations, 61 (3). 106. ISSN 0944-2669
Abstract
We introduce Lagrangian mean curvature flow with boundary in Calabi–Yau manifolds by defining a natural mixed Dirichlet-Neumann boundary condition, and prove that under this flow, the Lagrangian condition is preserved. We also study in detail the flow of equivariant Lagrangian discs with boundary on the Lawlor neck and the self-shrinking Clifford torus, and demonstrate long-time existence and convergence of the flow in the first instance and of the rescaled flow in the second.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. This is an author produced version of an article published in Calculus of Variations and Partial Differential Equations. Uploaded in accordance with the publisher's self-archiving policy. |
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: | 01 Apr 2022 14:21 |
Last Modified: | 18 May 2023 09:14 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s00526-022-02229-0 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:185344 |