Harmonic maps between surfaces : with a special chapter on conformal mappings / Jürgen Jost

This monograph gives a fairly complete and self-contained account of the results on harmonic maps between surfaces. It shows the variety of methods and the interplay of different fields in the theory of harmonic maps, in particular, differential geometry and nonlinear analysis in the large. This treatment contains several simplifications and unifications compared to the presentations of these results in their original papers.
After presenting the definitions of harmonic maps from several points of view and geometric consideration, the author discusses existence and uniqueness of harmonic maps and some a priori estimates. In this book the existence of harmonic diffeomorphisms and harmonic coordinates is also considered by using the above estimates. The final chapter gives some applications of harmonic maps between surfaces. (MathSciNet)