Discrete Riemann surfaces: Linear discretization and its convergence

Alexander Bobenko, Mikhail Skopenkov

Research output: Contribution to journalArticlepeer-review


We develop linear discretization of complex analysis, originally introduced by R. Isaacs, J. Ferrand, R. Duffin, and C. Mercat. We prove convergence of discrete period matrices and discrete Abelian integrals to their continuous counterparts. We also prove a discrete counterpart of the Riemann–Roch theorem. The proofs use energy estimates inspired by electrical networks.
Original languageEnglish (US)
Pages (from-to)217-250
Number of pages34
JournalJournal fur die Reine und Angewandte Mathematik
Issue number720
StatePublished - Aug 19 2014
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2022-06-03
Acknowledgements: The first author was partially supported by the DFG Collaborative Research Center SFB/TR 109 “Discretization in Geometry and Dynamics”. The second author was partially supported by the President of the Russian Federation grant MK-5490.2014.1, by “Dynasty” foundation, and by the Simons–IUM fellowship. Part of the work on this paper was done during the stay of the second author at King Abdullah University of Science and Technology in Saudi Arabia.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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