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Classification of
convex ancient free-boundary curve-shortening flows in the
disc
Theodora Bourni and Mat Langford |
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Vol. 16 (2023), No. 9, 2225–2240
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Abstract |
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Using a combination of direct geometric methods and an analysis of the linearization of the flow about the horizontal bisector, we prove that there exists a unique (modulo rotations about the origin) convex ancient curve-shortening flow in the disc with free boundary on the circle. This appears to be the first result of its kind in the free-boundary setting. |
Keywords
curve-shortening flow, free-boundary, ancient solutions
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Mathematical Subject Classification
Primary: 53E10
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Milestones
Received: 10 November 2021
Revised: 23 February 2022
Accepted: 29 March 2022
Published: 11 November 2023
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Authors |
| Theodora Bourni | |
| Department of Mathematics University of Tennessee Knoxville, TN United States |
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| Mat Langford | |
| Mathematical Sciences
Institute Australian National University Canberra Australia |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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