Surveys in Differential Geometry

Volume 9 (2004)

Discrete analytic functions: An exposition

Pages: 241 – 273



L. Lovász (Microsoft Research, One Microsoft Way, Redmond, WA 98052, U.S.A.)


Harmonic and analytic functions have natural discrete analogues. Harmonic functions can be defined on every graph, while analytic functions (or, more precisely, holomorphic forms) can be defined on graphs embedded in orientable surfaces. Many important properties of the “true” harmonic and analytic functions can be carried over to the discrete setting.

Full Text (PDF format)