Minimising L [to the power of p] distortion for mappings between annuli : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics at Massey University, Albany, New Zealand

Abstract

When deforming or distorting one material object into another, for various physical reasons the final deformation is expected to minimise some sort of energy functional. Classically, the theory of quasiconformal mappings provides us with a theory of distortion, yielding some limited results concerning minimising the maximal distortion. The calculus of variations is aimed at extremising certain kinds of functionals (such as the integral of the gradient squared or of distortion over a region in the complex plane). This thesis investigates quasiconformal and related mappings between annuli. introduces some novel results, and outlines some conjectures for further research.