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For questions regarding harmonic functions.

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Find sufficient and necessary conditions on $f$ in which the level curve $f(x,y)=0$ implies ... [closed]

Let $f:ℝ²→ℝ$ be an arbitrary harmonic function. A level curve in two dimensions is a curve on which the value of a function $f(x,y)$ is a constant. My question is: Find sufficient and necessary condit …