On Kiyoshi Oka’s unpublished papers in 1943

In 1943 from September to December Kiyoshi Oka wrote a series of papers numbered from VII to XI, as the research reports to Teiji Takagi (then, Professor of Tokyo Imperial University), in which he solved affirmatively the so-called Levi Problem (Hartogs’ Inverse Problem termed by Oka) for unramified Riemann domains over $\mathbb{C}^n$. This problem which had been left open for more than thirty years then, was the last one of the Three Big Problems summarized by Behnke–Thullen 1934. The papers were hand-written in Japanese, consist of pp. 108 in total, and have not been published by themselves. The aim of the present article is to provide an English translation of the most important, last paper (Part II) with preparation (Part I). At the end of Part I we will discuss a problem which K. Oka left and is still open.

Keywords

coherence, Oka, Levi problem, Hartogs’ inverse problem, several complex variables

2010 Mathematics Subject Classification

01A60, 32A99, 32E30

Full Text (PDF format)

For the 120th anniversary of Kiyoshi Oka’s birth.

The author is sincerely grateful to Mr. H. Oka for the kind agreement of the English translation of the unpublished paper XI of [26] as the copyright holder, and to “Oka Kiyoshi Collection, Library of Nara Women’s University” for the resources.

Research supported in part by Grant-in-Aid for Scientific Research (C) 19K03511.

Received 5 July 2021

Published 16 August 2022