Classification of convex ancient free boundary mean curvature flows in the ball
Theodora Bourni, Mat Langford
TL;DR
This paper proves the uniqueness of convex ancient mean curvature flows with free boundary conditions in a ball across all dimensions, showing that such flows are essentially unique up to rotations and time shifts.
Contribution
It establishes the existence and uniqueness of convex ancient free boundary mean curvature flows in the ball for all dimensions, a significant advancement in geometric flow theory.
Findings
Uniqueness of convex ancient free boundary mean curvature flows in the ball.
Existence of such flows in every dimension.
Flows are unique modulo rotations and time translations.
Abstract
We prove that there exists, in every dimension, a unique (modulo rotations about the origin and time translations) convex ancient mean curvature flow in the ball with free boundary on the sphere.
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 · Geometry and complex manifolds · Mathematical Dynamics and Fractals