Ancient solutions for flow by powers of the curvature in R2
Publication Name
Calculus of Variations and Partial Differential Equations
Abstract
We construct a new compact convex embedded ancient solution of the κα flow in R2, α∈(12,1) that lies between two parallel lines. Using this solution we classify all convex ancient solutions of the κα flow in R2, for α∈(23,1). Moreover, we show that any non-compact convex embedded ancient solution of the κα flow in R2, α∈(12,1) must be a translating solution.
Open Access Status
This publication may be available as open access
Volume
61
Issue
2
Article Number
44
Funding Number
2105026
Funding Sponsor
Simons Foundation