Geodesic surface

  • Thread starter mhill
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  • #1
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Main Question or Discussion Point

if we have or can have geodesic curves minimizing the integral [tex] \sqrt (g_{ab}\dot x_a \dot x_b ) [/tex] is there a theory of 'minimizing surfaces or Geodesic surfaces' that minimize the Area or a surface ?,
 

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  • #2
gel
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I don't know about the general theory, but in Euclidean space this is http://en.wikipedia.org/wiki/Plateau%27s_problem" [Broken].
For space-time surfaces, in Minkowski space, it is similar to the simplest (non-quantized) http://en.wikipedia.org/wiki/Nambu-Goto_action" [Broken] except I assume you would be maximizing the "area".
 
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  • #3
robphy
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http://math.rice.edu/~polking/Math410/ [Broken] lists some examples.
 
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