KnowraHarmonic functionLinked fromLinked fromThe 17 pages that link to Harmonic function, each with the reason it gives.All 17Broader topic 4Related 9Narrower topic 2Compared with 2Complex analysisRelated: Real and imaginary parts of holomorphic functions are harmonic, but harmonic functions need not arise globally this way.Scalar fieldRelated: Harmonic functions are scalar fields with a distinctive local averaging property.Cauchy–Riemann equationsRelated: The equations imply that both components of a sufficiently smooth holomorphic function are harmonic.Elliptic operatorRelated: Harmonic functions are the basic solutions of the Laplace equation.Hadamard three-circle theoremRelated: Linear interpolation in log-radius comes from harmonic functions on an annulus.Jensen's formulaRelated: Away from zeros, the logarithmic modulus of a holomorphic function is harmonic.Schwarz reflection principleRelated: Real and imaginary parts of holomorphic extensions provide reflected harmonic extensions.Borel–Carathéodory theoremRelated: The real part of every holomorphic function is harmonic, supplying the theorem’s scalar control.Weyl's lemmaRelated: The lemma concludes that the distribution is represented by a function of this kind.