Cong Yao
Doctor of Philosophy, (Mathematics)
Study Completed: 2019
College of Sciences
Citation
Thesis Title
Minimisation of Mean Exponential Distortions and Teichmuller Theory
Read article at Massey Research Online: 
In deformations of material objects, physical laws give the final state minimising an energy functional and solving a typically non-linear partial differential equation. Mr Yao's research exploited novel connections between minimisation of distortion functionals and harmonic mappings. He investigated the explicit duality, between the harmonic maps approach to Teichmüller theory and the classical theory via minimisers of mean distortion and posits interpolation between these cases via Lp- minimisers. The results find applications to theoretical materials science and critical phase phenomena, as distortion functionals are natural measures of change in a system and address fundamental questions relating to microstructure and length scales.
Supervisors
Distinguished Professor Gaven Martin
Distinguished Professor Peter Schwerdtfeger
Associate Professor Alexander Melnikov