Sheldon Chang will continue his work on minimal surfaces. The origins of this subject lie in the study of soap films. Because of the surface tension in these films they naturally form minimal surfaces. That is, for a given boundary they have minimum area of all surfaces with this boundary. In the mathematical theory this property translates into a curvature property of the surface. Nowadays surfaces with zero mean curvature are referred to as minimal surfaces. Chang's research is concerned with the existence of minimal surfaces within a given surface. This is a very natural and important extension since such minimal surfaces provide a natural extension of the notion of geodesic, that is, minimum length path, in the surface. Chang has developed remarkable expertise in the rather inaccessible topic of geometric measure theory. Many of the most exciting developments in minimal surface theory have made use of this theory. He will build on recent work of others concerning integral currents and varifolds to attack these problems. The major focus of the work will be to study the topological type of these minimal surfaces and the size of their set of singularities. Probably the most difficult hurdle to overcome will be to find techniques which apply to the high codimensional situation.
