Area-Minimizing Currents mod 2Q: Linear Regularity Theory

We establish a theory of Q -valued functions minimizing a suitable generalization of the Dirichlet integral. In a second paper the theory will be used to approximate efficiently area minimizing currents mod(p) when p = 2Q , and to establish a first general partial regularity theorem for every p in any dimension and codimension . © 2020 Wiley Periodicals LLC.