An invitation to n-harmonic hyperelasticity

We give an account of some recent developments in which quasiconformal theory and nonlinear elasticity share common problems of compelling mathematical interest. Geometric function theory is currently a field of enormous activity where the language and general framework of nonlinear elasticity is extremely fruitful and significant. As this interplay developed n-harmonic deformations became valid and well acknowledged as generalization of conformal mappings in Rⁿ. We have also found a place for n-harmonic deformations in the theory of hyperelasticity. J. Ball's fundamental paper [5] accounts for the principles of hyperelasticity and sets up mathematical problems. In presenting the recent advances we have relied on a few new existing articles [2, 3, 28, 29, 30, 31, 32, 33].