Notes on Minimal Surfaces and Differential Forms I

Besides the obvious application of minimal surface theory to the study of soap films, there are a number of other physical systems in which the theory of minimal surfaces has a sometimes surprising applicability. To this author, a rekindling of an interest in minimal surfaces came from the (recent in 1991) realization that the topological patterns associated with hydrodynamic instabilities and wakes can be related to minimal surfaces. Minimal surfaces can be interpreted as limit sets which are the results of a (perhaps irreversible) process decaying into a stationary state. A number of theories and hopefully interesting observations are presented below, utilizing the ideas of minimal surfaces in 4 dimensions.

Also see the Maple printout for the Minimal surface generated by the holomorphic Madelbrot generator.


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