Hans Grauert

Hans Grauert in Moscow , 1966

Hans Grauert (born February 8, 1930 in Haren / Ems ; † September 4, 2011 in Göttingen ) was considered one of the most important German mathematicians of the post-war period. His specialty was the function theory of several variables.

life and work

Grauert attended high school in Meppen from 1946 to 1949 and studied (after a semester in Mainz , where he learned mathematical logic) from 1949 at the Westphalian Wilhelms University (WWU) in Münster with Heinrich Behnke , where he worked in 1954 with the work Kählersche Metrik in holomorphism , which was published two years later in the Mathematische Annalen . As a member of the Behnke School, he was able to benefit from the excellent contacts in France at the time, in particular with Henri Cartan . Before his dissertation he also studied in 1953 with the topologist Beno Eckmann at the ETH Zurich . In 1955 he became an assistant professor in Münster, where he completed his habilitation in 1957 before going to the Institute for Advanced Study for a year in 1957/58 . In 1959 he worked at the Institute des Hautes études Mathematiques (IHES) near Paris .

From September 1959 until his retirement he was full professor in Göttingen as the successor to Carl Ludwig Siegel . In Göttingen he formed a very active large school of complex analysis. He has also held visiting professorships, including in Princeton and Paris.

Together with Henri Cartan and Reinhold Remmert , a close collaborator since the 1950s, Grauert was the main engine of the boom that the complex analysis of several variables took after the Second World War .

In 1965 he gave another proof of the mordell presumption for functional bodies (originally proven by Yurij Manin ). In addition, he was busy u. a. with hyperbolic geometry and non-Archimedean function theory. Grauert also considered new geometric structures for use in physics ( Statistical geometry and spacetime , Comm. Math. Phys. Vol. 49, 1976, p. 155, and Nachr. Akad. Wiss. Göttingen 1976), as well as about the formalism of quantum theory.

From 1969 he was editor of the Mathematische Annalen . In 1966 he was invited speaker at the International Congress of Mathematicians in Moscow ( On non-Archimedean analysis , with Remmert) and in Edinburgh in 1958 ( The Riemann surfaces of the function theory of several variables ). In 1962 he gave a plenary lecture at the ICM in Stockholm ( The meaning of the Levi problem for analytical and algebraic geometry ).

His daughter Ulrike Peternell is also a mathematician, married to the mathematician Thomas Peternell , who did his doctorate under Grauert. Further doctoral students are Günther Trautmann , Klas Diederich (Wuppertal), Wolfgang Fischer (Bremen), Gudrun Kalmbach , Klaus Fritzsche , Ingo Lieb , Helmut Reckziegel (Cologne), Oswald Riemenschneider (Hamburg), Jürgen Spilker (Freiburg), Heinz Spindler (Osnabrück) .

Honors

• Member of the Academies of Sciences in Göttingen , Halle ( Leopoldina ), Mainz and Munich
• Foreign member of the Russian Academy of Sciences (2006)
• Honorary doctorate from the Universities of Bayreuth, Bochum and Bonn
• In 1991 Grauert was the first recipient of the Staudt Prize .
• 2008 honorary member of the DMV
• 2008 Georg Cantor Medal

Works

• Selected papers , 2 volumes, Springer Verlag 1994
• with Reinhold Remmert: Theory of Stein's Spaces , Springer 1977 (1979, 2004)
• this: Analytical place algebras , Springer 1971
• this: Coherent analytic sheaves , Springer 1984
• with Klaus Fritzsche: Introduction to the function theory of several complex variables , Springer 1974, English 1976
• with Klaus Fritzsche: From holomorphic functions to complex manifolds , Springer 2002
• with Hans-Christoph Grunau: Linear Algebra and Analytical Geometry. Oldenbourg Publishing House, 1999
• with Ingo Lieb (vol. 1,3), Wolfgang Fischer (vol. 2): differential and integral calculus , 3 vol., Springer, Heidelberger Taschenbücher, 1967/68 and 1977 (vol. 1: Functions of a real variable, vol. 2: Differential calculus in several variables. Differential equations, Vol. 3: Integration theory. Curve and surface integrals)
• Characterization of the holomorphic complete complex spaces , mathem. Annalen, Vol. 129, 1955, p. 233
• with Remmert: On the theory of modifications I , Math. Annalen 1955
• with Remmert: Plurisubharmonic functions in complex spaces , Mathematische Zeitschrift 1956
• with Remmert: Complex spaces , Mathematische Annalen, Vol. 136, 1958
• with Remmert: Singularities of Complex Manifolds and Riemannian Regions , Mathematische Zeitschrift 1957
• Characterization of the holomorphic areas by the complete Kähler metric , Mathem. Annalen 1953, dissertation
• About modifications and exceptional analytical sets , mathem. Annals Vol. 146, 1962
• Mordell's conjecture about rational points on algebraic curves and function bodies , Publications Mathématiques de l'IHES, Vol. 25, 1965, pp. 131–149
• A theorem of analytical sheaf theory and modular spaces of complex structures , Publications Mathématiques de l'IHES, Vol. 5, 1960, pp. 5–64 , with corrections here: [1]
• with Andreotti: Théorèmes de finitude pour la cohomologie des espaces complexes , Bulletin de la Société Mathématique de France, Vol. 90, 1962, pp. 193-259

literature

• I. Bauer, F. Catanese , Y. Kawamata, T. Peternell, Siu (Eds.): Complex geometry: Collection of papers dedicated to Hans Grauert. Springer, Berlin 2002.
• Reinhold Remmert: The algebraization of the function theory. DMV Mitteilungen, 1993, No. 4, pp. 13-18, doi: 10.1515 / dmvm-1993-0406 (freely accessible)
• Reinhold Remmert: Complex Analysis in Sturm und Drang. Karl Georg Christian von Staudt Prize for Hans Grauert (laudation), DMV Mitteilungen, 1993, No. 1, pp. 5–13, doi: 10.1515 / dmvm-1993-0104 (freely accessible),
• Georg Schumacher , On the development of complex analysis in Germany from the end of the 19th century to the beginning of the 1970s , Annual Report DMV Vol. 98, 1996, pp. 41-133, online
• Alan Huckleberry Hans Grauert (1930-2011) , Annual Report DMV, Volume 115, 2013, Issue 1, pp. 21–45, doi: 10.1365 / s13291-013-0061-7 , Arxiv (freely accessible)
• Alan T. Huckleberry, Hans Grauert: Mathematician Pur , DMV Mitteilungen, 2008, Volume 16, Issue 2, pp. 75-77, doi: 10.1515 / dmvm-2008-0033 (freely accessible), the like. Notices AMS 2009
• Alan Huckleberry, Thomas Peternell et al., Tribute to Hans Grauert , Notices AMS, May 2014, pp. 472-483, online

Web links

• John J. O'Connor, Edmund F. Robertson :  Hans Grauert. In: MacTutor History of Mathematics archive .
• Literature by and about Hans Grauert in the catalog of the German National Library
• Hans Grauert in the Mathematics Genealogy Project (English)
• Photos showing Hans Grauert ( Oberwolfach Photo Collection )

Individual evidence

1. ↑ Characterization of the holomorphic areas by the complete Kählersche Metrik , Mathematische Annalen, Volume 131, 1956, pp. 38-75, online . See Fabrizio Catanese: Obituary for Hans Grauert. February 8, 1930 - September 4, 2011 , yearbook of the Göttingen Academy of Sciences, 2012, issue 2, pp. 308–315, doi: 10.1515 / jbg-2012-0029 .
2. ↑ Hans Grauert in the Mathematics Genealogy Project (English)
3. ^ Foreign members of the Russian Academy of Sciences since 1724. Hans Grauert. Russian Academy of Sciences, accessed August 20, 2015 (Russian).