Nonsmooth hypersurfaces with smooth Levi curvature

In R3R3, Lipschitz continuous viscosity solutions to the KK-prescribed Levi curvature equation are smooth and strictly pseudoconvex if KK is smooth and strictly positive; see [5]. We show here that in R2n+1R2n+1, n>1n>1, a similar result does not hold; that is, we prove the existence in Cn+1Cn+1, n>1n>1, of nonsmooth pseudoconvex hypersurfaces with smooth Levi curvature.