420 citations · 1.3k across the 61 of their papers we have counts for
71 papers
Constant mean curvature surfaces from ring patterns: Geometry from combinatorics
Alexander I. Bobenko, Tim Hoffmann, Nina Smeenk
We define discrete constant mean curvature (cmc) surfaces in the three-dimensional Euclidean and Lorentz spaces in terms of sphere packings with orthogonally intersecting circles.…
Spherical and hyperbolic orthogonal ring patterns: integrability and variational principles
Alexander I. Bobenko
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their r…
Dimers and M-Curves: Limit Shapes from Riemann Surfaces
Alexander I. Bobenko, Nikolai Bobenko
We present a general approach for the study of dimer model limit shape problems via variational and integrable systems techniques. In particular we deduce the limit shape of the Az…
Minimal reflection surfaces in Combinatorics of curvature lines and minimal surfaces based on fundamental pentagons
Alexander I. Bobenko, Sebastian Heller, Nicolas Schmitt
We study compact minimal surfaces in the 3-sphere which are constructed by successive reflections from a minimal -gon -- so-called minimal reflection surfaces. The minimal -g…
Dimers and M-Curves
Alexander I. Bobenko, Nikolai Bobenko, Yuri B. Suris
In this paper we develop a general approach to dimer models analogous to Krichever's scheme in the theory of integrable systems. We start with a Riemann surface and the simplest ge…
Isothermic tori with one family of planar curvature lines and area constrained hyperbolic elastica
Alexander I. Bobenko, Tim Hoffmann, Andrew O. Sageman-Furnas
In 1883, Darboux gave a local classification of isothermic surfaces with one family of planar curvature lines using complex analytic methods. His choice of real reduction cannot co…