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

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Link to publisher version (DOI)

http://dx.doi.org/10.1007/s00526-021-02145-9