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