The first-order Gamma-limit of the rescaled elastica functional is a sum of integer multiples of 2 pi, one per curvature concentration point, for immersed open curves with fixed endpoints and tangents and for closed curves of prescribed length.
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Concentration effects and $\Gamma$-limit for the elastica functional for open and closed curves
The first-order Gamma-limit of the rescaled elastica functional is a sum of integer multiples of 2 pi, one per curvature concentration point, for immersed open curves with fixed endpoints and tangents and for closed curves of prescribed length.