solution of the Levi problem

The Levi problem is the problem of characterizing domains of holomorphy by a local condition on the boundary that does not involve holomorphic functionsMathworldPlanetmath themselves. This condition turned out to be pseudoconvexity.


An open set GCn is a domain of holomorphy if and only if G is pseudoconvex.

The forward direction (domain of holomorphy implies pseudoconvexity) is not hard to prove and was known for a long time. The opposite direction is really what’s called the solution to the Levi problem.


  • 1 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
Title solution of the Levi problem
Canonical name SolutionOfTheLeviProblem
Date of creation 2013-03-22 14:31:11
Last modified on 2013-03-22 14:31:11
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 6
Author jirka (4157)
Entry type Theorem
Classification msc 32T05
Classification msc 32E40
Related topic Pseudoconvex
Related topic DomainOfHolomorphy
Defines Levi problem