  In this paper, we first prove that the totally real discs lying in certain
Levi flat hypersurfaces are polynomially convex. As applications we prove that
the totally real discs lying in the boundary of certain polynomial polyhedra
are polynomially convex. We also provide an if and only if condition for
polynomial convexity of totally real discs lying in the boundary of Hartog's
triangle. We also provide sufficient conditions on general compact subsets
lying on those hypersurfaces for polynomial convexity.

Complex Variables