On Kiyoshi Oka’s unpublished papers in 1943

Abstract

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 $\C^n$. 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.