Tromba will carry out research into the theory of minimal surfaces combining methods from the theory of variational calculus and non-linear analysis. His attention will be focussed mainly on questions related to Plateau's problem which is connected with finding minimal surfaces with a given boundary. In particular he will investigate how extensive a Morse theory can hold for the Plateau problem in Euclidean three space. In its original form Morse theory is concerned with the relationships between the critical points of a smooth function on a compact manifold and the topology of that manifold. Also, for higher genus surfaces, an investigation of index theory will be carried out.
