http://en.wikipedia.org/wiki/Minimal_surface
Ref: The first figure with soap film at right.
What is surface parametrization or references? How is it connected to the
helicoid/catenoid ? Thanks.
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Well there is no general parametrization this depends on the shape of the border of the surface! – flawr Sep 16 '14 at 18:57
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@flawr For particular border defined as a helix is there one? – Narasimham Sep 16 '14 at 19:42
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I think you need on the one hand a closed border and on the other hand a criterion which you like to minimize. (There is a whole list in the WP article you cited.) – flawr Sep 16 '14 at 19:50
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@flawr A criterion other than minimum area is needed? ; Also one more clarification of local surface minimality.. what if we take a closed minimum perimeter line around a hole of the multiply connected Costa surface and let a minimum area film span it as a diaphragm ? – Narasimham Sep 16 '14 at 21:46