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1993 Computing discrete minimal surfaces and their conjugates
Ulrich Pinkall, Konrad Polthier
Experiment. Math. 2(1): 15-36 (1993).


We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of fixed or free boundary curves in $\R^3$, $\Sph ^3$ and $\H^3$. The algorithm makes no restriction on the genus and can handle singular triangulations.

Additionally, we present an algorithm that, starting from a discrete harmonic map, gives a conjugate harmonic map. This can be applied to the identity map on a minimal surface to produce its conjugate minimal surface, a procedure that often yields unstable solutions to a free boundary value problem for minimal surfaces. Symmetry properties of boundary curves are respected during conjugation.


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Ulrich Pinkall. Konrad Polthier. "Computing discrete minimal surfaces and their conjugates." Experiment. Math. 2 (1) 15 - 36, 1993.


Published: 1993
First available in Project Euclid: 3 September 2003

zbMATH: 0799.53008
MathSciNet: MR1246481

Primary: 53A10
Secondary: 49Q05 , 58E12 , 65D17

Rights: Copyright © 1993 A K Peters, Ltd.

Vol.2 • No. 1 • 1993
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