Let A and B be circular annuli in the complex plane and consider the Dirichlet energy integral of $j-$degree mappings between A and B. Then we minimize this energy integral. The minimizer is a $j-$degree harmonic mapping between annuli A and B provided it exits. If such a harmonic mapping does not exist, then the minimizer is still a $j-$degree mapping which is harmonic in A'⊂ A and it is a squeezing mapping in its complementary annulus A''=A A. Such a result is an extension of the certain result of Astala, Iwaniec and Martin {astala2010}.
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David Kalaj (2024) studied this question.
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