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Tr. Mat. Inst. Steklova, 2018, Volume 302, Pages 202–213 (Mi tm3920)  

Bounded discrete holomorphic functions on the hyperbolic plane

I. A. Dynnikov

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: 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.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968518030093

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 302, 186–197

Bibliographic databases:

UDC: 517.962.22+517.547.9
Received: April 2, 2018

Citation: I. A. Dynnikov, “Bounded discrete holomorphic functions on the hyperbolic plane”, Topology and physics, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 302, MAIK Nauka/Interperiodica, Moscow, 2018, 202–213; Proc. Steklov Inst. Math., 302 (2018), 186–197

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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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