On two methods for approximating minimal surfaces in parametric form

Author:
Takuya Tsuchiya

Journal:
Math. Comp. **46** (1986), 517-529

MSC:
Primary 49D20; Secondary 49F10, 65E05

MathSciNet review:
829622

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Abstract: Two methods for approximating minimal surfaces in parametric form are considered. One minimizes the area of the surface, and the other the energy of the surface. The convergence of the algorithm of the first method is proved. The application of the second method to the approximation of conformal maps is examined. Several examples of computations are given.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1986-0829622-1

Keywords:
Minimal surface,
parametric form,
parametrization,
conformal map,
relaxation method,
the Douglas-Rado solution of the classical Plateau problem

Article copyright:
© Copyright 1986
American Mathematical Society