Surveys in Differential Geometry
Volume 9 (2004)
An excursion into geometric analysis
Pages: 83 – 146
This is a guided tour through some selected topics in geometric analysis. Most of the results here can be found in the literature but some are new and do not appear elsewhere. We have chosen to illustrate many of the basic ideas as they apply to the theory of minimal surfaces. This is, in part, because minimal surfaces is, if not the oldest, then certainly one of the oldest areas of geometric analysis dating back to Euler's work in the 1740’s and in fact many of the basic ideas in geometric analysis originated in the study of minimal surfaces. In any case, the ideas apply to a variety of different fields and we will mention some of these as we go along.