Post Closed as "too localized" by Andres Caicedo, Willie Wong, Yemon Choi, Pete L. Clark, David Hansen

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Relation between complex analysis and harmonic functions function theory

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

  • Holomorphic functions and complex functions are analytic;
  • Cauchy's integral formula on 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 sugests suggest that there are conections connections between these two areas and i think that i can I would like to ask: how can each one of these theorys theories be used do to develop the other?

PS: I'm realy really sorry for my realy really bad englishEnglish.

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There are some theorems in harmonic functions theory that resembles results in complex analysis, like:

  • Holomorphic functions and complex functions are analytic;
  • Cauchy's integral formula on complex analysis and mean value theorem in harmonic 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 sugests that there are conections between these two areas and i think that i can ask: how can each one of these theorys be used do develop the other?

PS: I'm realy sorry for my realy bad english.

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