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
** For citizens of Germany, see also German nationality law
**Ge ...
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, structure, space, models, and change.
History
On ...
. 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 form a ...
, 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 vers ...
s in a series of four papers in 1907–1909. He did his thesis at
Berlin
Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...
, where he worked under
Hermann Schwarz
Karl Hermann Amandus Schwarz (; 25 January 1843 – 30 November 1921) was a German mathematician, known for his work in complex analysis.
Life
Schwarz was born in Hermsdorf, Silesia (now Jerzmanowa, Poland). In 1868 he married Marie Kummer, ...
. He was an
extraordinary professor
Academic ranks in Germany are the titles, relative importance and power of professors, researchers, and administrative personnel held in academia.
Overview
Appointment grades
* (Pay grade: ''W3'' or ''W2'')
* (''W3'')
* (''W2'')
* (''W2'', ...
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 wel ...
from 1910 to 1914, then an
ordinary professor
Academic ranks in Germany are the titles, relative importance and power of professors, researchers, and administrative personnel held in academia.
Overview
Appointment grades
* (Pay grade: ''W3'' or ''W2'')
* (''W3'')
* (''W2'')
* (''W2'', ...
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 In complex analysis, a branch of mathematics, the Koebe 1/4 theorem states the following:
Koebe Quarter Theorem. The image of an injective analytic function f:\mathbf\to\mathbb from the unit disk
\mathbf onto a subset of the complex plane con ...
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
Ludwig Georg Elias Moses Bieberbach (; 4 December 1886 – 1 September 1982) was a German mathematician and Nazi.
Biography
Born in Goddelau, near Darmstadt, he studied at Heidelberg and under Felix Klein at Göttingen, receiving his doctorate ...
in 1916, and the function
providing a tight example for this theorem became known as the
Koebe function In complex analysis, a branch of mathematics, the Koebe 1/4 theorem states the following:
Koebe Quarter Theorem. The image of an injective analytic function f:\mathbf\to\mathbb from the unit disk
\mathbf onto a subset of the complex plane con ...
.
Awards
* 1922,
Ackermann–Teubner Memorial Award
See also
*
Koebe groups
*
Midsphere
In geometry, the midsphere or intersphere of a polyhedron
In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices.
A convex poly ...
*
Riemann mapping theorem
In complex analysis, the Riemann mapping theorem states that if ''U'' is a non-empty simply connected space, simply connected open set, open subset of the complex plane, complex number plane C which is not all of C, then there exists a biholomorphy ...
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