Theory of Stein Spaces

Hans Grauert (b. 1930 in Harem /Ems, Germany) and Reinhold Remmert (b. 1930 in Osnabruck, Germany) met at the University of Munster, where they both studied mathematics and physics from 1949 to 1954. In 1950 they were invited by Heinrich Behnke and Karl Stein to attend their "Oberseminar", which was held on Saturdays, for 2 hours from 9 a.m. Five years after the tragic events of World War 2, Behnke's old friend Henri Cartan visited Munster. His lecture on recent developments in the theory of "Several Complex Variables" was a real eye-opener for the young students and had a strongly formative influence on them: indeed this was to determine the course of their scientific research careers from then on. In June 1954 Grauert and Remmert received their respective doctorates from the University of Munster. In 1957 they both became lecturer (Privatdozent) there. In 1959 resp. 1960, Grauert and Remmert were appointed full professors at Gottingen resp. Erlangen. The original German edition of "Theory of Stein Spaces" was written at a time when complex spaces, coherent analytic sheaves and the so-called Theorems A and B had already become established notions and theorems. Dedicated to Karl Stein, the book was published in 1977, and the English edition was to follow in 1979. The first announcement of the book, in Springer's promotion, consisted of the picture reproduced on the inside cover flap of this book, taken during the boat trip of the annual Bonn Arbeitstagung some time earlier, showing three men on a boat, with the minimalistic caption "Grundlehren 227".

• A. Sheaf Theory.- B. Cohomology Theory.- I. Coherence Theory for Finite Holomorphic Maps.- II. Differential Forms and Dolbeault Theory.- III. Theorems A and B for Compact Blocks ?m.- IV. Stein Spaces.- V. Applications of Theorems A and B.- VI. The Finiteness Theorem.- VII. Compact Riemann Surfaces.- Table of Symbols.- Addendum.- Errors and Misprints.

"Theory of Stein Spaces provides a rich variety of methods, results, and motivations - a book with masterful mathematical care and judgement. It is a pleasure to have this fundamental material now readily accessible to any serious mathematician." J. Eells in Bulletin of the London Mathematical Society (1980) "Written by two mathematicians who played a crucial role in the development of the modern theory of several complex variables, this is an important book." J.B. Cooper in Internationale Mathematische Nachrichten (1979)