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Minimal surfaces from circle patterns: Geometry from combinatorics

Alexander I. Bobenko·Tim Hoffmann·Boris A. Springborn
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Abstract

We suggest a new definition for discrete minimal surfaces in terms of sphere packings with orthogonally intersecting circles. These discrete minimal surfaces can be constructed from Schramm's circle patterns. We present a variational principle which allows us to construct discrete analogues of some classical minimal surfaces. The data used for the construction are purely combinatorial--the combinatorics of the curvature line pattern. A Weierstrass-type representation and an associated family are derived. We show the convergence to continuous minimal surfaces.

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Alexander I. Bobenko, Tim Hoffmann, Boris A. Springborn. 2004-10-07. Minimal surfaces from circle patterns: Geometry from combinatorics. https://arxiv.org/abs/math/0305184

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