An estimate of the density at the boundary of an integral current modulo $v$

Abstract:

An inequality is obtained which bounds the density at $z \in {{\mathbf {R}}^n}$ of the boundary of a $k + 1$ dimensional integral current modulo $\nu \;{(S)^\nu }$ by the density of ${(S)^\nu }$ at z. Also, the concept of boundary tangent developed in [3] is shown to be in agreement with Federer’s concept of a measuretheoretic exterior normal if $\nu = 0$ and S is obtained by integration over an ${\mathfrak {L}^n}$ measurable subset of ${{\mathbf {R}}^n}$.