Interior regularity for stationary two-dimensional multiple valued maps


$Q$-valued maps minimizing a suitably defined Dirichlet energy were introduce by Almgren in his proof of the optimal regularity of area minimizing currents in any dimension and codimension. In this talk I will discuss the extension of Almgren’s result to stationary $Q$-valued maps in dimension $2$.

This is joint work with Jonas Hirsch (Leipzig).