Singular sets for curvature equation of order k

We consider the removability of singular sets for the curvature equations of the form Hk[u]=ψ, which is determined by the kth elementary symmetric function, in an n-dimensional domain Ω. We prove that, for 1⩽k⩽n−1 and a compact set K whose (n−k)-dimensional Hausdorff measure is zero, any generalized solution to the curvature equation on Ω∖K is always extendable to a generalized solution on the whole domain Ω.