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