Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 33

On a simple method to compute polygonal minimal surfaces

M. Hinze

Given a closed polygonal contour with N+3 vertices in the q-dimensional euklidean space there is a one-to-one correspondence between the roots of the gradient of Shiffman`s function and minimal surfaces spanned by the polygon. We derive an explicit expression for the gradient of the discrete Shiffman function and assure that each root of this function also is approximately a zero of the gradient of Shiffman`s function. Using quasi-newton -methods and variants of Newton`s Method, several examples of minimal surfaces are computed.

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