A Measure Theoretic Approach to Higher Codimension Mean Curvature Flows

We develop a generalization of the theory of varifolds and use it in the asymptotic study of a sequence of Ginzburg-Landau systems. These equations are reaction-diffusion type, nonlinear partial differential equations, and the main object of our study is the renormalized energy related to these systems. Under suitable density assumptions, we show convergence to a Brakke flow by mean curvature. The proof is based on a suitable generalization of the theory of varifolds and on the analysis of the gradient Young measures associated to the solutions of the system.