Discrete complex analysis on planar quad-graphs

@article{Bobenko2016DiscreteCA,
  title={Discrete complex analysis on planar quad-graphs},
  author={A. Bobenko and Felix Gunther},
  journal={arXiv: Complex Variables},
  year={2016},
  pages={57-132}
}
We develop further a linear theory of discrete complex analysis on general quad-graphs, extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on the medial graph leads to generalizations as well as to new proofs of previously known discrete analogs of classical theorems. New results include in particular discretizations of Green’s first identity and Cauchy’s integral formula for the derivative of a… Expand
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