Paul Koebe (15 February 1882 – 6 August 1945) was a 20th-century
German
German(s) may refer to:
* Germany (of or related to)
**Germania (historical use)
* Germans, citizens of Germany, people of German ancestry, or native speakers of the German language
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**Ger ...
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
. His work dealt exclusively with the
complex numbers
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the for ...
, his most important results being on the
uniformization of
Riemann surface
In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed ve ...
s in a series of four papers in 1907–1909. He did his thesis at
Berlin
Berlin is Capital of Germany, the capital and largest city of Germany, both by area and List of cities in Germany by population, by population. Its more than 3.85 million inhabitants make it the European Union's List of cities in the European U ...
, where he worked under
Hermann Schwarz. He was an
extraordinary professor at
Leipzig
Leipzig ( , ; Upper Saxon: ) is the most populous city in the German state of Saxony. Leipzig's population of 605,407 inhabitants (1.1 million in the larger urban zone) as of 2021 places the city as Germany's eighth most populous, as ...
from 1910 to 1914, then an
ordinary professor at the
University of Jena
The University of Jena, officially the Friedrich Schiller University Jena (german: Friedrich-Schiller-Universität Jena, abbreviated FSU, shortened form ''Uni Jena''), is a public research university located in Jena, Thuringia, Germany.
The un ...
before returning to Leipzig in 1926 as an ordinary professor. He died in Leipzig.
He conjectured the
Koebe quarter theorem on the radii of disks in the images of injective functions, in 1907. His conjecture became a theorem when it was proven by
Ludwig Bieberbach in 1916, and the function
providing a tight example for this theorem became known as the
Koebe function.
Awards
* 1922,
Ackermann–Teubner Memorial Award
See also
*
Koebe groups
*
Midsphere
In geometry, the midsphere or intersphere of a polyhedron is a sphere which is tangent to every edge of the polyhedron. That is to say, it touches any given edge at exactly one point. Not every polyhedron has a midsphere, but for every convex ...
*
Riemann mapping theorem
In complex analysis, the Riemann mapping theorem states that if ''U'' is a non-empty simply connected open subset of the complex number plane C which is not all of C, then there exists a biholomorphic mapping ''f'' (i.e. a bijective holomorphic ma ...
References
External links
*
{{DEFAULTSORT:Koebe, Paul
1882 births
1945 deaths
People from Luckenwalde
20th-century German mathematicians
University of Jena faculty
Leipzig University faculty
Humboldt University of Berlin alumni
People from the Province of Brandenburg