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Ancient solutions for flow by powers of the curvature in R2

Journal Article


Abstract


  • We construct a new compact convex embedded ancient solution of the ���� flow in R2, �����(12,1) that lies between two parallel lines. Using this solution we classify all convex ancient solutions of the ���� flow in R2, for �����(23,1). Moreover, we show that any non-compact convex embedded ancient solution of the ���� flow in R2, �����(12,1) must be a translating solution.

Publication Date


  • 2022

Citation


  • Bourni, T., Clutterbuck, J., Nguyen, X. H., Stancu, A., Wei, G., & Wheeler, V. M. (2022). Ancient solutions for flow by powers of the curvature in R2. Calculus of Variations and Partial Differential Equations, 61(2). doi:10.1007/s00526-021-02145-9

Scopus Eid


  • 2-s2.0-85124389148

Volume


  • 61

Issue


  • 2

Place Of Publication


Abstract


  • We construct a new compact convex embedded ancient solution of the ���� flow in R2, �����(12,1) that lies between two parallel lines. Using this solution we classify all convex ancient solutions of the ���� flow in R2, for �����(23,1). Moreover, we show that any non-compact convex embedded ancient solution of the ���� flow in R2, �����(12,1) must be a translating solution.

Publication Date


  • 2022

Citation


  • Bourni, T., Clutterbuck, J., Nguyen, X. H., Stancu, A., Wei, G., & Wheeler, V. M. (2022). Ancient solutions for flow by powers of the curvature in R2. Calculus of Variations and Partial Differential Equations, 61(2). doi:10.1007/s00526-021-02145-9

Scopus Eid


  • 2-s2.0-85124389148

Volume


  • 61

Issue


  • 2

Place Of Publication