We consider the problem of minimizing {formula omitted} for a planar curve having fixed initial and final positions and directions. The total length L is free. Here s is the variable of arclength parametrization, K(s) is the curvature of the curve and ¿>0 a parameter. 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. We prove that if for a certain choice of boundary conditions there is no global minimizer, then there is neither a local minimizer nor a geodesic.
We finally give properties of the set of boundary conditions for which there exists a solution to the problem.

Original language | English |
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Publisher | s.n. |
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Number of pages | 28 |
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Publication status | Published - 2012 |
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Name | arXiv.org |
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Volume | 1203.3089 [math.OC] |
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