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 functions themselves. This condition turned out to be pseudoconvexity.
An open set is a domain of holomorphy if and only if 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|
|Date of creation||2013-03-22 14:31:11|
|Last modified on||2013-03-22 14:31:11|
|Last modified by||jirka (4157)|