Research objectives and content
During the last few years I have been working in the general area of Geometric Analysis. I am interested in the study of area minimizing and minimal submanifolds, harmonic maps, and other related variational problems, where insight on existence and /or regularity properties of the solutions can be attained by bringing together tools from the theory of Partial Differential Equations, Geometric Measure Theory, and Diffential Geometry. Amongst other things, I propose to examine some questions concerning minimizing the area functional in certain classes of lagrangian submanifolds of a given symplectic manifold and the mean curvature flow. Training content (objective, benefit and expected impact)
At this point of my mathematical career I have gained some experience in the fields of Geometric Measure Theory and Elliptic Partial Differential Equations, but I feel I need to improve my understanding of the more (differential) geometric aspects, and of other types of PDEs (in particular parabolic ones, in view of my interest in the mean curvature flow). I would hope to use a TMR grant to pursue these objectives. The Mathematische Institut at the University of Bonn is one of the leading centers in the field of Geometric Partial Differential Equations, thus the experience gained there would certainly contribute greatly to my further development as a researcher.