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Q: Mathematica & minimal surfaces

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  • Subject: [mg1675] Q: Mathematica & minimal surfaces
  • From: Zorro <berriz at>
  • Date: Tue, 11 Jul 1995 05:57:20 -0400
  • Organization: Harvard University, Cambridge, Massachusetts

Hi.  This is a simple question for those more familiar with
Mathematica's capabilities and/or differential geometry than I am.

I've seen many examples of minimal surfaces drawn using Mathematica,
but it seems that Mathematica is of little help if all one starts with
is the parametrization of the curve, without an explicit
parametrization for the corresponding minimal surface.  (Here's where
my total ignorance of differential geometry shines through: I'm
assuming that there is no straightfoward way of computing the
parametrization of the minimal surface given the parametrization of
the generating curve).

It seems that if one wants to have Mathematica draw a given curve's
minimal surface, one must first somehow figure out, basically "by
hand", the parametrization of this surface and feed it to Mathematica,
which then plots it like any other parametrized surface.  Is this
correct?  Or is it the case that given a parametrization t -> f(t) of
an arbitrary curve living in R^3, there's a "simple way" (i.e. either
built-in or package functions) in Mathematica to display the minimal
surface corresponding to this curve?  (Note that I'm not interested in
a functional parametrization of the minimal surface in question, only
in an image on the screen, therefore numerical solutions are fine for
my purposes.)

Thanks for your help,


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