The proposer intends to devote most of his research effort on problems in the analytic theory of minimal submanifolds. In particular, questions about the nature of singularities will be addressed. Under consideration, will be the question of what types of singularities can occur, and whether singularities can be perturbed away, by perturbing the data (that is, the boundary, or the background metric), especially in codimension one. Similar problems in the theory of harmonic maps, and complete metrics of constant scalar curvature will be studied.
