Geodesic
Bounded discrete holomorphic functions on the hyperbolic plane
Informatics and Automation, Topology and physics, Tome 302 (2018), pp. 202-213.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that, for the discretization of complex analysis introduced earlier by S. P. Novikov and the present author, there exists a rich family of bounded discrete holomorphic functions on the hyperbolic (Lobachevsky) plane endowed with a triangulation by regular triangles whose vertices have even valence. Namely, it is shown that every discrete holomorphic function defined in a bounded convex domain can be extended to a bounded discrete holomorphic function on the whole hyperbolic plane so that the Dirichlet energy be finite. 
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     author = {I. A. Dynnikov},
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I. A. Dynnikov. Bounded discrete holomorphic functions on the hyperbolic plane. Informatics and Automation, Topology and physics, Tome 302 (2018), pp. 202-213. https://geodesic-test.mathdoc.fr/item/TRSPY_2018_302_a8/

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