Besicovitch-Federer projection theorem for subspaces of complex vector space

Abstract:

In this talk, we will discuss a generalisation of the classical Besicovitch–Federer projection theorem to complex vector spaces. The classical Besicovitch–Federer theorem states that if A is a subset of R^n, then one can determine whether A is purely m-unrectifiable by examining the projections of A onto m-dimensional real subspaces of R^n. We will review the classical theorem and explore how the same type of information can be obtained by considering projections onto m-dimensional complex subspaces.