Analytic polyhedron

In mathematics, especially several complex variables, an analytic polyhedron is a subset of the complex space of the form
where is a bounded connected open subset of, are holomorphic on and is assumed to be relatively compact in. If above are polynomials, then the set is called a polynomial polyhedron. Every analytic polyhedron is a domain of holomorphy and it is thus pseudo-convex.
The boundary of an analytic polyhedron is contained in the union of the set of hypersurfaces
An analytic polyhedron is a Weil polyhedron, or Weil domain if the intersection of any of the above hypersurfaces has dimension no greater than.