TY - JOUR
T1 - Discrete Riemann surfaces: Linear discretization and its convergence
AU - Bobenko, Alexander
AU - Skopenkov, Mikhail
N1 - 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.
PY - 2014/8/19
Y1 - 2014/8/19
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/678540
UR - https://www.degruyter.com/document/doi/10.1515/crelle-2014-0065/html
UR - http://www.scopus.com/inward/record.url?scp=84990229111&partnerID=8YFLogxK
U2 - 10.1515/crelle-2014-0065
DO - 10.1515/crelle-2014-0065
M3 - Article
SN - 1435-5345
VL - 720
SP - 217
EP - 250
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 720
ER -