Area minimising currents: singular set rectifiability and tangent cone uniqueness

Paul Minter, Princeton University

Abstract: One of the great achievements of geometric measure theory is Almgren’s work (1983) on area minimising n-currents, showing that such objects are smoothly embedded away from a (generally unavoidable) singular set of dimension at most n-2. In this talk, I will discuss recent work with Camillo De Lellis (IAS) and Anna Skorobogatova (Princeton) showing that the singular set is countably (n-2)-rectifiable, with unique tangent cones at almost every point.