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

We prove a contraction property of certain classes of smooth functions, whose absolute 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 for harmonic mappings in the complex plane.