For small curvature oscillation, length-penalized and length-constrained elastic flows in a cone converge exponentially to circular arcs, while the free elastic flow converges smoothly to an expanding circular arc.
Dall’Acqua, C.-C
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Length-constrained, length-penalised and free elastic flows of planar curves inside cones
For small curvature oscillation, length-penalized and length-constrained elastic flows in a cone converge exponentially to circular arcs, while the free elastic flow converges smoothly to an expanding circular arc.