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”The Levi problem was first solved by Oka”ね
YUM-TONG SIUは、例のSIUさんか
URLﾘﾝｸ(projecteuclid.org)
BULLETIN OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 84, Number 4, July 1978
PSEUDOCONVEXTTY AND THE PROBLEM OF LEVI
BY YUM-TONG SIU
The Levi problem is a very old problem in the theory of several complex
variables and in its original form was solved long ago. However, over the
years various extensions and generalizations of the Levi problem were proposed
and investigated. Some of the more general forms of the Levi problem
still remain unsolved. In the past few years there has been a lot of activity in
this area. The purpose of this lecture is to give a survey of the developments
in the theory of several complex variables which arise from the Levi problem.
We will trace the developments from their historical roots and indicate the
key ideas used in the proofs of these results wherever this can be done
intelligibly without involving a lot of technical details. For the first couple of
sections of this survey practically no knowledge of the theory of several
complex variables is assumed on the part of the reader. However, as the
survey progresses, an increasing amount of knowledge of the theory of several
complex variables is assumed.
Table of Contents
1. Domains of holomorphy
2. The original Levi problem
3. Stein manifolds
4. Locally Stein open subsets
5. Increasing sequence of Stein open subsets
6. The Serre problem
7. Weakly pseudoconvex
P484
The Levi problem was first solved by Oka. He did the case n = 2 in [67]
and the general case in [68]. The case of a general n was also solved at the
same time independently by Bremermann [8] and Norguet [66].