Analytic polyhedron

In mathematics, especially several complex variables, an analytic polyhedron is a subset of the complex space Cⁿ of the form

where D is a bounded connected open subset of Cⁿ and f j are holomorphic on D. If f j 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 the union of the set of hypersurfaces

An analytic polyhedron is a Weil polyhedron, or Weil domain if the intersection of k hypersurfaces has dimension no greater than 2n-k.