There are some theorems in harmonic function theory that resemble results in complex analysis, like:

- Holomorphic functions and complex functions are analytic;
- Cauchy's integral formula in complex analysis and the mean value theorem in harmonic function theory;
- The principle of maximum and minimum that works for harmonic and holomophic functions.
- The real and imaginary parts of a holomorphic function are harmonic;

These results suggest that there are connections between these two areas and I would like to ask: how can each of these theories be used to develop the other?

PS: I'm really sorry for my really bad English.

Harmonic functions from a complex analysis viewpoint, by Sheldon Axler. (Google it to find an online version.) – Charles Staats Jan 16 '11 at 0:51