In the summer of , he enrolled in the University of Mainz. Karl Stein was already a well-established professor in the group and Friedrich Hirzebruch was a rising star. Grauert had entered, probably by chance, one of the most stimulating mathematical atmospheres in postwar Germany. At the age of twenty-seven he obtained and His email address is ahuck cplx. His email address is thomas. He illustrated his point by saying that when you play the music of a master composer, you are not supposed to substitute for it a variation of your own.
Needless to say, given all the effort and time I Grauert, Stein, and Remmert, While Three fundamental research monographs were working on my Ph.
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Gunning at Princeton, I spent a coauthors he published textbooks in the areas of great deal of time poring over the original papers real and complex analysis. In the entire generation of mathematicians in several particular, he guided more than forty Ph. Two of them, Ingo goldmines to explore and work on.
His mathe- For the Levi problem Grauert introduced his matical influence will last forever. How to construct global holomorphic functions on ab- Yum-Tong Siu stractly defined complex manifolds and spaces is one of the most fundamental problems in Hans Grauert in Memoriam complex geometry. It is the method of minimizing Dirichlet the characterization of holomorphically complete integrals on Riemann surfaces, which is motivated complex spaces.
It was my first experience pre- by electrostatic potentials. I spent a great technique of constructing holomorphic functions deal of time reading the paper and reorganizing it was a breakthrough of fundamental importance. His email address is siu math.
Grauert and Siu, Although later in the early s Forster- ometry, thereby extending the latter to the setting Knorr and Kiehl-Verdier gave simpler proofs of of singular spaces.
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The golden finiteness theorems for p-pseudoconvex and q- foundational period of the modern theory of sev- pseudoconcave spaces and coherent sheaves with eral complex variables started with the work of cohomological codimension conditions and to the schools of Behnke, Oka, Cartan, Serre, Stein, construct compactifications of pseudoconcave Remmert, Andreotti, and many others and culmi- ends.
Grauert developed Runge approximation and international conferences Grauert mentored techniques for functions with values in holomor- an entire generation of young mathematicians phic fiber bundles to prove the equivalence between working on the theory of several complex vari- topological and holomorphic fiber bundles over ables.
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He set the research agenda in the field by Stein spaces. Since then he has invited best rigorously proved cases of the Oka principle. Grauert The direct image theorem of Grauert gives the was a man of very few words. Yet his concise, coherence of the direct images of coherent sheaves to-the-point professional comments carried great under proper holomorphic maps. Grauert proved impact. Grauert was very kind, affable, and gener- it by introducing a smoothing method to relate ous. Whenever he was in the company of young the norm estimates of cochains in two different mathematicians, he always inspirationally shared Stein coverings for the same cohomology class without any hesitation his mathematical ideas with in order to guarantee the convergence of power anybody within earshot.
Grauert was an intellectual giant.
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Those of us who had the good fortune of coming under his tutelage are not only awed by his brilliant mind as a mathematician but inspired, too, by his personal qualities. He was truly a shining example of integrity and magnanimity. I really wanted to meet him in person because I was strongly impressed by his masterpieces.
Not to mention the great I still recall with nostalgic fondness those casual achievements, including the solution of the Levi after-dinner conversations in the lounge area out- problem on complex manifolds see [G3] , I highly side the library. I especially enjoyed my admits a holomorphically convex neighborhood visit in , when Grauert was compiling his own whenever the normal bundle is seminegative. Fujiki had keep him up to date concerning the impact of given to me after I finished reading [G5]. To my his work on the field. We conversed daily about great pleasure I received a positive answer.
His recounting of the glad if you can come. On Sundays Grauert eventually came up with the choice of the Gaussian took Siu and me in his Mercedes to the suburbs. He then told me that Around noon on a sunny day, we saw the mountain when he was a student he was very interested on which Gauss measured relatively big triangles. He began to focus his attention on The next day Siu gave a seminar talk. It was the Takeo Ohsawa is professor of mathematics at Nagoya Univer- good fortune of mathematics that the accidental sity, Japan.
His email address is ohsawa math. I was happy to hear this because I had already submitted a paper solving it affirmatively see [O]. Why not capture this wonderful chance! Allowed by Grauert, I did it in ten or fifteen minutes because I could skip some part of the L2 -theory. All of this happened in a lecture room where very large portraits of Klein and Hilbert were hung. At that time, Grauert was ally arrived at a result [OT] which recently turned interested in the study of Kobayashi hyperbolicity, out to be useful for many purposes.
Anyway, the complex variables. Grauert in Niedersachsen, Germany.
He passed away on had already been in close contact with Grothendieck September 4, , leaving the mathematical world at the end of the s, culminating with their with an extraordinary legacy in complex analysis work on the direct image theorem for coherent and analytic geometry.
I would like to share here sheaves in the algebraic and analytic settings, [G3] a few recollections of my encounters with him and [G4], respectively. Although he was obviously during the last decades and some connections of not at all targeted, I remember that Grauert was a his work with my own research. I was a young Grauert introduced in [G8] the important concept student at that time, and on the detour of a of a jet metric, following previous work by Green naive question I had raised, he had to explain the and Griffiths [GG] on jet differentials.
His email metric is then just a hermitian metric on that sheaf; address is Jean-Pierre. Demailly ujf-grenoble.
In the same paper, Grauert and Riemenschneider conjectured that a compact analytic space is Moishezon if and only if it carries an almost positive coherent sheaf of rank 1; cf. By looking at all holomor- their harmonic counterparts. Enter the code below and hit Verify. Free Shipping All orders of Cash on Delivery Pay for your order in cash at the moment the shipment is delivered to your doorstep. Log In. Don't have an account? Sign Up. Update your profile Let us wish you a happy birthday! Add your birthday. Buy it Again. Make sure to buy your groceries and daily needs Buy Now.
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