Stability of weakly almost conformal mappings.

We prove a stability of weakly almost conformal mappings in $W^{1, p}(\Omega;\mathbf {R}^n)$ for $p$ not too far below the dimension $ n$ by studying the $ W^{1, p}$-quasiconvex hull of the set $\mathcal C_n $ of conformal matrices. The study is based on coercivity estimates from the nonlinear Hodge decompositions and reverse Hölder inequalities from the Ekeland variational principle. [ABSTRACT FROM AUTHOR]