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.
Theorem.
An open set G⊂Cn 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.
References
- 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 |