ArticleslgStudy

mathematics

Hans Grauert

Hans Grauert is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hans Grauert rather than just read about it. In short: Hans Grauert (8 February 1930 in Haren, Emsland, Germany – 4 September 2011) was a German mathematician. He is known for major works on several complex variables, complex manifolds and the application of sheaf theory in this area, which influenced later work in algebraic geometry.

Hans Grauert — main illustration
Hans Grauert — illustration

Key takeaways

  • Hans Grauert belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Hans Grauert to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Hans Grauert from memory before moving on to harder problems.

Reference excerpt

Hans Grauert (8 February 1930 in Haren, Emsland, Germany – 4 September 2011) was a German mathematician. He is known for major works on several complex variables, complex manifolds and the application of sheaf theory in this area, which influenced later work in algebraic geometry. Together with Reinhold Remmert he established and developed the theory of complex-analytic spaces.

Professorship Grauert attended school at the Gymnasium in Meppen before studying for a semester at the University of Mainz in 1949, and then at the University of Münster, where he was awarded his doctorate in 1954. He became professor at the University of Göttingen in 1958, as successor to C. L. Siegel. The lineage of this chair traces back through an eminent line of mathematicians: Weyl, Hilbert, Riemann, and ultimately to Gauss. Until his death, he was professor emeritus at Göttingen.

Awards Grauert was awarded a fellowship of the Leopoldina and the von Staudt Prize.

Publications Grauert, Hans (1994), Selected papers. Vol. I, II, Berlin, New York: Springer-Verlag, ISBN 978-3-540-57107-0, MR 1314425 with Klaus Fritzsche: Several Complex Variables, 1976; hbk{{citation}}: CS1 maint: postscript (link) Grauert, H.; Fritzsche, K. (6 December 2012). softcover reprint 2012. Springer. ISBN 978-1-4612-9874-8. with Klaus Fritzsche: Fritzsche, Klaus; Grauert, Hans (2002), From Holomorphic Functions to Complex Manifolds, Springer, ISBN 978-0-387-95395-3

See also Faltings' theorem Levi problem Grauert's approximation theorem

References

External links Hans Grauert at the Mathematics Genealogy Project photo of Hans Grauert at Oberwolfach

Illustrations

Hans Grauert illustration

Worked examples

Example 1 — a first encounter with Hans Grauert

Start with the simplest possible case. Write down what Hans Grauert claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hans Grauert before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hans Grauert ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hans Grauert

In research
Hans Grauert appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Hans Grauert in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Hans Grauert is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1930 births, 2011 deaths, 20th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Hans Grauert outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Hans Grauert” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Hans Grauert in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Hans Grauert means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Hans Grauert out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hans Grauert in simple terms?

Hans Grauert (8 February 1930 in Haren, Emsland, Germany – 4 September 2011) was a German mathematician. He is known for major works on several complex variables, complex manifolds and the application of sheaf theory in this area, which influenced later work in algebraic geometry.

Why does Hans Grauert matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hans Grauert?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hans Grauert.

Tags

  • 1930 births
  • 2011 deaths
  • 20th-century German mathematicians
  • 21st-century German mathematicians
  • Academic staff of the University of Göttingen
  • Complex analysts
  • German mathematician stubs
  • People from Emsland
  • University of Mainz alumni
  • University of Münster alumni

Keep exploring