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We consider the problem of minimizing L 0 1 + K(t) 2 dt for a planar curve having fixed initial and final positions and directions. Here K(t) is the curvature of the curve and the total length L is free. This problem comes from a model of geometry of vision due to Petitot, Citti and Sarti. We study existence of local and global minimizers for this problem.… (More)

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