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.
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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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