Minimal surfaces from circle patterns: Geometry from combinatorics

dc.creatorBobenko, Alexander I.
dc.creatorHoffmann, Tim
dc.creatorSpringborn, Boris A.
dc.date2003-05-13
dc.date2004-10-07
dc.date.accessioned2026-07-07T06:31:00Z
dc.date.available2026-07-07T06:31:00Z
dc.descriptionWe 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.description30 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.identifierhttps://arxiv.org/abs/math/0305184
dc.identifierhttp://arxiv.org/abs/math/0305184
dc.identifierAnn. of Math. 164:1 (2006), 231-264
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98490
dc.subjectDifferential Geometry
dc.subjectCombinatorics
dc.subject52C26, 53A10 (Primary) 53C42 (Secondary)
dc.titleMinimal surfaces from circle patterns: Geometry from combinatorics
dc.typetext

Files

Collections