Real and discrete holomorphy : Introduction to an algebraic approach
Metric Geometry
2016-08-16 v2 Complex Variables
Differential Geometry
Dynamical Systems
Abstract
We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is then possible to define an "amazing" notion of holomorphic functions on them, and show how rigid it is in some cases.
Cite
@article{arxiv.math/0407385,
title = {Real and discrete holomorphy : Introduction to an algebraic approach},
author = {Sylvain Barré and Abdelghani Zeghib},
journal= {arXiv preprint arXiv:math/0407385},
year = {2016}
}