Multiple minimizing functions?

  1. Is there any kind of uniqueness theorem for minimizing functions? What about when there are multiple minimizing path - say going from one pole of a sphere to the other end, you've got an infinite number of paths you could take. Does this just manifest itself when you go through and solve the problem, say like the solution is theta-independent?

    I can't think of another example right now, but this just popped in my head going over the Euler-Lagrange derivation for my Mechanics final
     
  2. jcsd
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