Ancient solutions for flow by powers of the curvature in R2

Theodora Bourni, Julie Clutterbuck, Xuan Hien Nguyen, Alina Stancu, Guofang Wei, Valentina Mira Wheeler

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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.

Original languageEnglish
Article number44
Number of pages14
JournalCalculus of Variations and Partial Differential Equations
Volume61
Issue number2
DOIs
Publication statusPublished - 2022

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