Topic class on minimal surfaces — lectures by Rick Schoen

This series of lecture notes were taken for the topic class on minimal surfaces given by Professor Rick Schoen in the Winter quarter of 2012 at Stanford. We kept the pace of these lectures by dates. These lectures start from basic materials on minimal surfaces, e.g. first and second variations, and monotonicity formulae, and then discuss several curvature estimates for minimal surfaces. Afterwards, the notes cover basic existence theory for minimal surfaces, e.g. the classical Plateau problem and the Sacks-Uhlenbeck theorem, and finally end up with a survey of the proof of the Willmore conjecture. The materials covered are very good examples for the application of methods from partial differential equations and calculus of variation. It is likely that we have numerous typos and mistakes here and there, and would appreciate it if these are brought to our attention.