Minimal surfaces from circle patterns: Geometry from combinatorics
| dc.creator | Bobenko, Alexander I. | |
| dc.creator | Hoffmann, Tim | |
| dc.creator | Springborn, Boris A. | |
| dc.date | 2003-05-13 | |
| dc.date | 2004-10-07 | |
| dc.date.accessioned | 2026-07-07T06:31:00Z | |
| dc.date.available | 2026-07-07T06:31:00Z | |
| dc.description | 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. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/math/0305184 | |
| dc.identifier | http://arxiv.org/abs/math/0305184 | |
| dc.identifier | Ann. of Math. 164:1 (2006), 231-264 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98490 | |
| dc.subject | Differential Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 52C26, 53A10 (Primary) 53C42 (Secondary) | |
| dc.title | Minimal surfaces from circle patterns: Geometry from combinatorics | |
| dc.type | text |