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.  2005 Elsevier Inc. All rights reserved.