solution of the Levi problem
The Levi problem is the problem of characterizing domains ofholomorphy by a local condition on the boundary that does not involveholomorphic functions themselves. This condition turned out tobe pseudoconvexity.
Theorem.
An open set is a domain of holomorphy ifand only if is pseudoconvex.
The forward direction (domain of holomorphy implies pseudoconvexity) isnot hard to prove and was known for a long time. The opposite directionis really what’s called the solution to the Levi problem.
References
- 1 Steven G. Krantz.,AMS Chelsea Publishing, Providence, Rhode Island, 1992.