Discrete Riemann Surfaces
Complex Variables
2008-02-13 v1 Mathematical Physics
Differential Geometry
math.MP
Abstract
We detail the theory of Discrete Riemann Surfaces. It takes place on a cellular decomposition of a surface, together with its Poincar\'e dual, equipped with a discrete conformal structure. A lot of theorems of the continuous theory follow through to the discrete case, we define the discrete analogs of period matrices, Riemann's bilinear relations, exponential of constant argument and series. We present the notion of criticality and its relationship with integrability.
Cite
@article{arxiv.0802.1612,
title = {Discrete Riemann Surfaces},
author = {Christian Mercat},
journal= {arXiv preprint arXiv:0802.1612},
year = {2008}
}