8 citations · 10 across the 3 of their papers we have counts for
10 papers
Minimal surfaces from circle patterns: Geometry from combinatorics
Alexander I. Bobenko, Tim Hoffmann, Boris A. 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 fro…
Computing Riemann Theta Functions
Bernard Deconinck, Matthias Heil, Alexander Bobenko +2
The Riemann theta function is a complex-valued function of g complex variables. It appears in the construction of many (quasi-) periodic solutions of various equations of mathemati…
Hyperbolic constant mean curvature one surfaces: Spinor representation and trinoids in hypergeometric functions
Alexander I. Bobenko, Tatyana V. Pavlyukevich, Boris A. Springborn
We present a global representation for surfaces in 3-dimensional hyperbolic space with constant mean curvature 1 (CMC-1 surfaces) in terms of holomorphic spinors. This is a modific…
Variational principles for circle patterns and Koebe's theorem
Alexander I. Bobenko, Boris A. Springborn
We prove existence and uniqueness results for patterns of circles with prescribed intersection angles in constant curvature surfaces. Our method is based on two new functionals--on…
Integrable systems on quad-graphs
Alexander I. Bobenko, Yuri B. Suris
We consider general integrable systems on graphs as discrete flat connections with the values in loop groups. We argue that a certain class of graphs is of a special importance in…
Hexagonal Circle Patterns and Integrable Systems. Patterns with Constant Angles
Alexander I. Bobenko, Tim Hoffmann
Hexagonal circle patterns with constant intersection angles are introduced and studied. It is shown that they are described by discrete integrable systems of Toda type. Conformally…