420 citations · 1.3k across the 61 of their papers we have counts for
10 papers · 1 filter
Orthogonal ring patterns in the plane
Alexander I. Bobenko, Tim Hoffmann, Thilo Rörig
We introduce orthogonal ring patterns consisting of pairs of concentric circles generalizing circle patterns. We show that orthogonal ring patterns are governed by the same equatio…
Convergence of discrete period matrices and discrete holomorphic integrals for ramified coverings of the Riemann sphere
Alexander I. Bobenko, Ulrike Bücking
We consider the class of compact Riemann surfaces which are ramified coverings of the Riemann sphere . Based on a triangulation of this covering of the sphere $\m…
Discrete Riemann surfaces based on quadrilateral cellular decompositions
Alexander I. Bobenko, Felix Günther
Our aim in this paper is to provide a theory of discrete Riemann surfaces based on quadrilateral cellular decompositions of Riemann surfaces together with their complex structure e…
Discrete complex analysis on planar quad-graphs
Alexander I. Bobenko, Felix Günther
We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete co…
The asymptotic behaviour of the discrete holomorphic map via the Riemann-Hilbert method
Alexander I. Bobenko, Alexander Its
We study the asymptotic behavior of the discrete analogue of the holomorphic map . The analysis is based on the use of the Riemann-Hilbert approach. Specifically, using the De…
Discrete Riemann surfaces: linear discretization and its convergence
Alexander Bobenko, Mikhail Skopenkov
We develop linear discretization of complex analysis, originally introduced by R. Isaacs, J. Ferrand, R. Duffin, and C. Mercat. We prove convergence of discrete period matrices and…
Hexagonal circle patterns with constant intersection angles and discrete Painleve and Riccati equations
S. I. Agafonov, A. I. Bobenko
Hexagonal circle patterns with constant intersection angles mimicking holomorphic maps z^c and log(z) are studied. It is shown that the corresponding circle patterns are immersed a…
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…
Hexagonal circle patterns and integrable systems: Patterns with the multi-ratio property and Lax equations on the regular triangular lattice
A. I. Bobenko, T. Hoffmann, Yu. B. Suris
Hexagonal circle patterns are introduced, and a subclass thereof is studied in detail. It is characterized by the following property: For every circle the multi-ratio of its six in…
Conformally symmetric circle packings. A generalization of Doyle spirals
Alexander I. Bobenko, Tim Hoffmann
From the geometric study of the elementary cell of hexagonal circle packings --- a flower of 7 circles --- the class of conformally symmetric circle packings is defined. Up to Moeb…