Experimental Mathematics

Computing discrete minimal surfaces and their conjugates

Ulrich Pinkall and Konrad Polthier

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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.

Article information

Experiment. Math., Volume 2, Issue 1 (1993), 15-36.

First available in Project Euclid: 3 September 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 49Q05: Minimal surfaces [See also 53A10, 58E12] 58E12: Applications to minimal surfaces (problems in two independent variables) [See also 49Q05] 65D17: Computer aided design (modeling of curves and surfaces) [See also 68U07]


Pinkall, Ulrich; Polthier, Konrad. Computing discrete minimal surfaces and their conjugates. Experiment. Math. 2 (1993), no. 1, 15--36. https://projecteuclid.org/euclid.em/1062620735

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