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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.
David Kalaj (Tue,) studied this question.
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