For let , i.e. the symmetric part of the polar decomposition of A. We consider the relation between two quasiregular mappings whose symmetric part of gradient are close. Our main result is the following. Suppose are Q-quasiregular mappings with for some and . There exists constant such that if then
Taking we obtain a special case of the quantitative rigidity result of Friesecke, James and Müller . Our main result can be considered as a first step in a new line of generalization of Theorem 1 of  in which Id is replaced by a mapping of non-trivial degree.
Cite this article
Andrew Lorent, Rigidity of pairs of quasiregular mappings whose symmetric part of gradient are close. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 1, pp. 23–65DOI 10.1016/J.ANIHPC.2014.08.003