Classification of convex ancient free boundary curve shortening flows in the disc
Theodora Bourni, Mat Langford
TL;DR
This paper classifies convex ancient solutions to the curve shortening flow within a disc, where the boundary is free on the circle, providing a comprehensive understanding of such flows.
Contribution
It offers a complete classification of convex ancient free boundary curve shortening flows in the disc, a novel result in geometric flow theory.
Findings
Complete classification of convex ancient solutions
Characterization of free boundary conditions
Insights into boundary behavior of flows
Abstract
We classify convex ancient curve shortening flows in the disc with free boundary on the circle.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Mathematical Dynamics and Fractals