User:DVD206/The Laplace-Beltrami operator and harmonic functions
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- a harmonic function is a twice continuously differentiable function f : U → R (where U is an open subset of Rn) which satisfies Laplace's equation.
- mean-value property
- The value of a harmonic function is a weighted average of its values at the neighbor vertices.
- maximum principle
- Corollary: the maximum (and the minimum) of a harmonic functions occurs on the boundary of the graph or the manifold.
- harmonic conjugate
- One can use the system of Cauchy Riemann equations
to define the harmonic conjugate
- analytic continuation
- Analytic continuation is an extension of the domain of a given analytic function.