Nonlinear elasticity problems on Carnot groups and quasiconformal analysis

It is known that the limit of a sequence of quasiconformal mappings, that is, homeomorphisms with bounded distortion whose distortion coefficients are jointly bounded, is either quasiconformal or a constant mapping. In this paper, it is shown that an analogous property holds, in the setting of Carnot groups of Heisenberg type, for a certain class of orientation-preserving homeomorphisms with finite distortion whose distortion function is integrable to a suitable power. This result is applied to the search for bijective solutions to variational problems analogous to nonlinear elasticity problems in irregular domains.