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We prove a contraction property of certain classes of smooth functions, whoseabsolute values of elements are log-hyperharmonic functions in the unit ball,thus extending the results of Kulikov to higher-dimensional space (GAFA(2022)). Moreover, by applying those results we get some new results forharmonic mappings in the complex plane.

Contraction property of certain classes of log-$\mathcal{M}-$subharmonic functions in the unit ball in $\mathbb{R}^n$