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,
are holomorphic on D and P is assumed to be relatively compact in D.[1] If
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 k of the above hypersurfaces has dimension no greater than 2n-k.[2]
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