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MathGroup Archive 1993

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minimal surfaces

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: minimal surfaces
  • From: xinwei at otter.stanford.edu (Sha Xin Wei)
  • Date: Tue, 23 Nov 93 16:51:13 -0800

Hi,

        there's a large body of literature on such problems.  My  
experience with it comes from the differential geometry, so may not  
suit your needs.  But some random references include:

\bibitem{} Pierre Pelce', Dynamics of Curved Fronts. Perspectives in  
Physics, Academic Press (1988).

\bibitem{} Sigurd Angenent, Shrinking Doughnuts.  Proceedings of the  
Conference on Elliptic and Parabolic Equations, Gregynog, Wales  
(August 1989).

\bibitem{} -------------, Multiphase thermomechanics with interfacial  
structure 2. evolution of an isothermal interface. preprint  (January  
1989) to appear ?.


\bibitem{} C.L. Epstein, Michael Gage, The curve shortening flow,  
Wave Motion: Theory, Modelling, and Computation. ed. A, Chorin, A.  
Majda. MSRI Publication 7 (198?) 15-59.

R. Osserman has a classic monograph on minimal surfaces, published by  
Dover.

Plus there's Ken Brakke's Surface Evolver program which you may  
anonymous-ftp from   geom.umn.edu.   Evolver is designed to minimize  
user-defined energies supported by a cell-complex (dimensions 0-3).    
It's quite general, has zillions of parameters, operators, runs on  
many computer, and is free.  The firtst vol. (last year) the  of  
Journal of Experimental Mathematics carried an article about Evolver,  
I believe.

Guess: your surfaces are very likely not minimal but constant mean  
curvature surfaces, if they minimize energies like pressure.

I presume you know that every minimal surface admits an integral  
representation, called the Weierstrass representation, so, given a  
suitable choice of a pair of meromorphic functions, you can generate  
whole families of minimal surfaces.  Of course, this places a heavy  
load on Mma's (N)Integrate.  But you may be able get more out of Mma  
now.  I tried this with Mma 1.0.

regards,
Sha Xin Wei
Stanford University





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