Experimental Mathematics

Numerical solution of soap film dual problems

Kenneth A. Brakke


The soap film problem is to minimize area, and its dual is to maximize the flux of a divergenceless bounded vector field. This paper discretizes the continuous problem and solves it numerically. This gives upper and lower bounds on the area of the globally minimizing film. In favorable cases, the method can be used to discover previously unknown films. No initial assumptions about the topology of the film are needed. The paired calibration or covering space model of soap films is used to enable representation of films with singularities.

Article information

Experiment. Math., Volume 4, Issue 4 (1995), 269-287.

First available in Project Euclid: 14 March 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: 49Q15: Geometric measure and integration theory, integral and normal currents [See also 28A75, 32C30, 58A25, 58C35] 65K10: Optimization and variational techniques [See also 49Mxx, 93B40]


Brakke, Kenneth A. Numerical solution of soap film dual problems. Experiment. Math. 4 (1995), no. 4, 269--287. https://projecteuclid.org/euclid.em/1047674388

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