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Dec 2, 2013 at 13:14 history edited Igor Khavkine CC BY-SA 3.0
added 239 characters in body
Jul 6, 2013 at 17:37 history edited Igor Khavkine CC BY-SA 3.0
Equations updated to MO2.0.
Jul 8, 2012 at 8:25 comment added Thomas Rot Thank you very much for this answer. I will ponder on it.
Jul 8, 2012 at 7:52 vote accept Thomas Rot
Jul 6, 2012 at 10:49 comment added alvarezpaiva Nice answer! Since you mentioned the har inverse problem, I'll complete your answer a bit bu mentioning that the problem of determining when a system of paths---one for every tangent direction---correspond to extremals of a variational problem is quite interesting and goes back to Darboux, Hilbert (his fourth problem, for example), Douglas (3 dimensions), and has been worked on by very many people. There is a huge gap between general results (your boxed theorem) and concrete cases like Hilbert's fourth problem.
Jul 6, 2012 at 10:16 history answered Igor Khavkine CC BY-SA 3.0