Generalized elastic translating solitons

Pámpano, Álvaro

doi:10.1090/proc/16651

Generalized elastic translating solitons
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by Álvaro Pámpano;

Proc. Amer. Math. Soc. 152 (2024), 1743-1753

DOI: https://doi.org/10.1090/proc/16651

Published electronically: January 26, 2024

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Abstract:

We study translating soliton solutions to the flow by powers of the curvature of curves in the plane. We characterize these solitons as critical curves for functionals depending on the curvature. More precisely, translating solitons to the flow by powers of the curvature are shown to be generalized elastic curves. In particular, focusing on the curve shortening flow, we deduce a new variational characterization of the grim reaper curve.

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