We study discrete complex analysis and potential theory on a large family of planar graphs,
the so-called isoradial ones. Along with discrete analogues of several classical results, we …

Proceedings of the International Congress of Mathematicians 2010 (ICM 2010) : Discrete
Complex Analysis and Probability Page 1 Proceedings of the International Congress of …

It was recognized, since the seminal papers of Arnold (Ann Inst Grenoble 16: 319–361,
1966) and Ebin-Marsden (Ann Math Ser 2 92 (1): 102–163, 1970), that Euler's equations are …

We define discrete flat surfaces in hyperbolic $3 $-space $\mathbb {H}^ 3$ from the
perspective of discrete integrable systems and prove properties that justify the definition. We …

We develop further a linear theory of discrete complex analysis on general quad-graphs,
extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete …

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 …

Two triangle meshes are conformally equivalent if for any pair of incident triangles the
absolute values of the corresponding cross-ratios of the four vertices agree. Such a pair can …

Two triangle meshes are conformally equivalent if their edge lengths are related by scale
factors associated to the vertices. Such a pair can be considered as preimage and image of …

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 …

This paper defines a theory of conformal parametrization of digital surfaces made of surfels
equipped with a normal vector. The main idea is to locally project each surfel to the tangent …