Classification of compact convex ancient solutions of the planar affine normal flow
Mohammad N. Ivaki
TL;DR
This paper proves that the only compact convex ancient solutions to the planar affine normal flow are contracting ellipses, providing a complete classification of such solutions in this geometric flow.
Contribution
It establishes a unique classification result for ancient solutions in the planar affine normal flow, showing they must be contracting ellipses.
Findings
Only contracting ellipses are compact convex ancient solutions.
Complete classification of ancient solutions in the planar affine normal flow.
No other shapes can be ancient solutions under this flow.
Abstract
We prove that the only compact convex ancient solutions of the planar affine normal flow are contracting ellipses.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Advanced Differential Equations and Dynamical Systems