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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
PII: S 0025-5718(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