[ Home ] [ About Us ] [ Research ] [ People ] [ Publications ] [ News ] [ Other Info ] [ Impressum ]
Sfb288 logo Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 587


Minimal surfaces from circle patterns: Geometry from combinatorics

A.I. Bobenko, T. Hoffmann, B. Springborn

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.


No PostScript version available.


Copyright © 1999 Sfb 288, Mathematics 8-5, Strasse des 17 Juni 136, TU-Berlin, 10623 Berlin
[ Home ] [ About Us ] [ Research ] [ People ] [ Publications ] [ News ] [ Other Info ] [ Impressum ]