Minimal surfaces from circle patterns: Geometry from combinatorics

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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.
30 pages, many figures, some in reduced resolution. v2: Extended introduction. Minor changes in presentation. v3: revision according to the referee's suggestions, improved & expanded exposition, references added, minor mistakes corrected

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Differential Geometry, Combinatorics, 52C26, 53A10 (Primary) 53C42 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/98490

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0305184
 http://arxiv.org/abs/math/0305184
 Ann. of Math. 164:1 (2006), 231-264

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arXiv