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Let $\mathbb{A}$ and $\mathbb{B}$ be circular annuli in the complex plane and consider the Dirichlet energy integral of $j-$degree mappings between $\mathbb{A}$ and $\mathbb{B}$. Then we minimize this energy integral. The minimizer is a $j-$degree harmonic mapping between annuli $\mathbb{A}$ and $\mathbb{B}$ provided it exits. If such a harmonic ma...
