Discrete Riemann Surfaces

Details Discrete Riemann Surfaces Discrete Riemann Surfaces

2008-02-12

arxiv.org/abs/0802.1612v1

Handbook of Teichm\"uller theory. Vol. I, Eur. Math. Soc., Z\"urich (Ed.) (2007) 541--575

Mathematics

Complex Variables

Scientific paper

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.

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