Generalized elastic translating solitons
Copyright policy )Generalized elastic translating solitons
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.
- The University of Texas System United States
Mathematics - Differential Geometry, translating solitons, Differential Geometry (math.DG), Flows related to mean curvature, FOS: Mathematics, generalized elastic curves, Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces, grim reaper, curve-shortening flow
Mathematics - Differential Geometry, translating solitons, Differential Geometry (math.DG), Flows related to mean curvature, FOS: Mathematics, generalized elastic curves, Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces, grim reaper, curve-shortening flow
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