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 ∈ R n z \in {{\mathbf {R}}^n} of the boundary of a k + 1 k + 1 dimensional integral current modulo ν ( S ) ν \nu \;{(S)^\nu } by the density of ( S ) ν {(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 ν = 0 \nu = 0 and S is obtained by integration over an L n {\mathfrak {L}^n} measurable subset of R n {{\mathbf {R}}^n} .