Chapitre D'ouvrage Année : 2007

Discrete Riemann Surfaces

Résumé

We detail the theory of Discrete Riemann Surfaces. It takes place on a cellular decomposition of a surface, together with its Poincaré 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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Dates et versions

hal-00250897 , version 1 (12-02-2008)

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Identifiants

Citer

Christian Mercat. Discrete Riemann Surfaces. Athanase Papadopoulos. Handbook of Teichmüller theory. Vol. I, Eur. Math. Soc., Zürich, pp.541--575, 2007, IRMA Lect. Math. Theor. Phys., 11, 978-3-03719-029-6. ⟨10.4171/029⟩. ⟨hal-00250897⟩
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