Affine Self-similar solutions of the affine curve shortening flow I: The degenerate case
Chengjie Yu, Feifei Zhao
TL;DR
This paper classifies affine self-similar solutions of the affine curve shortening flow in the Euclidean plane, especially focusing on the degenerate case, and introduces new special solutions.
Contribution
It provides a complete classification of affine self-similar solutions and describes new solutions in the degenerate case, advancing understanding of the flow's behavior.
Findings
All affine self-similar solutions are characterized up to affine transformations.
New special solutions for the affine curve shortening flow are discovered.
Descriptions of solutions in the degenerate case are provided.
Abstract
In this paper, we consider affine self-similar solutions for the affine curve shortening flow in the Euclidean plane. We obtain the equations of all affine self-similar solutions up to affine transformations and solve the equations or give descriptions of the solutions for the degenerate case. Some new special solutions for the affine curve shortening flow are found.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Mathematical Dynamics and Fractals · Geometry and complex manifolds