Editing Harmonic function (section)

===Harmonic functions on manifolds===
Harmonic functions can be defined on an arbitrary [[Riemannian manifold]], using the [[Laplace–Beltrami operator]] {{math|Δ}}. In this context, a function is called ''harmonic'' if 
<math display="block">\ \Delta f = 0.</math>
Many of the properties of harmonic functions on domains in Euclidean space carry over to this more general setting, including the mean value theorem (over [[geodesic]] balls), the maximum principle, and the Harnack inequality.  With the exception of the mean value theorem, these are easy consequences of the corresponding results for general linear [[elliptic partial differential equation]]s of the second order.