Unstable Periodic Discrete Minimal Surfaces

in: Nonlinear Partial Differential Equations, S. Hildebrandt and H. Karcher (Eds.) Springer Verlag (2002), pp. 127-143.

Konrad Polthier


In this paper we define the new alignment energy for non-conforming triangle meshes, and describes its use to compute unstable conforming discrete minimal surfaces. Our algorithm makes use of the duality between conforming and non-conforming discrete minimal surfaces which was observed earlier. In first experiments the new algorithm allows us the computation of unstable periodic discrete minimal surfaces of high numerical precision. The extraordinary precision of the discrete mesh enables us to compute the index of several triply periodic minimal surfaces.

Full Preprint: (.pdf 2.7 MB, .ps.zip 6.2 MB)