Herbert Grötzsch

Camillo Herbert Grötzsch (born May 21, 1902 in Döbeln ; † May 15, 1993 in Halle ) was a German mathematician who mainly dealt with function theory and graph theory.

Herbert Grötzsch with Horst Tietz (standing) on ​​his 86th birthday in Halle

Life

Camillo Herbert Grötzsch was born in Döbeln in 1902 . His father Emil Camillo Grötzsch, who received his doctorate from Sophus Lie in 1898 , was a mathematics teacher, most recently at the secondary school in Crimmitschau as senior director. Grötzsch attended the Realgymnasien in Döbeln and Crimmitschau and studied mathematics at the University of Jena from 1922 to 1926 with Paul Koebe , whom he also followed to the University of Leipzig , where he received his doctorate in 1929 as Koebe's assistant (“On conformal mapping of infinitely multiple connected simple areas with finitely many accumulation boundary components "). In 1931 he completed his habilitation at the University of Giessen . There he was an assistant from 1930 and then a private lecturer , but was dismissed in 1935 because he refused membership in the SA when the “young steel helmet” was forcibly incorporated . Until 1939 he worked for J. C. Poggendorff's concise dictionary in Leipzig and was then drafted into the artillery . After serving at the front, he was used in the homeland service after a kidney disease in 1942 and worked in 1944 in Göttingen at the Aerodynamic Institute on the calculation of jet engines . Since the University of Giessen was initially closed by the American occupation forces after the end of the Second World War , he worked at the University of Marburg from 1945 , where he first became an assistant, then an assistant and in 1947 an extraordinary professor. From 1948 he was a professor at the University of Halle , where he stayed until his retirement in 1967. From 1959 he was a member of the German Academy of Sciences Leopoldina . In 1967 he received the National Prize of the GDR, second class.

Grötzsch graph

Grötzsch is best known for his work on geometric function theory in the 1930s. In particular, he was the founder of the theory of quasi-conformal mapping (from 1928). While infinitesimal circles are mapped onto circles in conformal mappings, they are mapped more generally on ellipses in quasi- conformal mappings. The concept of quasi- conformal images, which is based on elementary geometric considerations, then proved to be very effective in the hands of Grötzsch, Lars Ahlfors , Oswald Teichmüller and others, in order to tackle extreme problems of conformal images that were previously classified as very difficult.

Several concepts in the theory of conformal and quasi-conformal mapping are named after Grötzsch. The unit disk from which an interval [0, r] is removed is called the Grötzsch area or Grötzschring . Grötzsch showed that this area has the maximum modulus among all ring areas that arise from the unit disk, if a compact is removed there, which contains the zero point and a point of magnitude r. The corresponding extremal problem is also called the Grötzsch problem , the Grötzsch function describes the module of this area as a function of r. The Grötzsch equation gives an estimate of the modulus of a ring area through the modulus of two partial rings. This inequality is important in the complex dynamics.

During his military service and after the war, he mainly dealt with combinatorics (graph theory) and elementary number theory. In 1959 he proved that every triangle-free plane graph can be colored with three colors. The " Grötzsch graph " is a non-flat example of a triangle-free graph that can only be colored with at least four colors. After 1960 he didn't publish anything. Lipman Bers gave the celebratory lecture on his 75th birthday .

From 1951 Grötzsch was married to Annemarie Jung, the daughter of the Halle mathematician Heinrich Jung , with whom he had three children.

literature

• Reiner Kühnau: Herbert Grötzsch in memory . Annual report of the German Mathematicians Association, volume. 99, 1997, pp. 122-145 (1997)
• ders. Some recent developments in quasi-conformal mapping . Annual report DMV 1992
• Horst Tietz : Herbert Grötzsch in Marburg . Annual report of the German Mathematicians Association, Vol. 99, 1997, pp. 146–148

See also

• Grötzsch's theorem (function theory)
• Grötzsch's theorem (graph theory)

Web links

• Entry on Herbert Grötzsch in the Catalogus Professorum Halensis
• Photos from Oberwolfach
• Grötzsch Graph at Weisstein

Remarks

1. ↑ The "ö" is pronounced stretched.
2. ↑ Before that, he had tried Konrad Knopp's in Tübingen , who, in his own words, treated him rather condescendingly.
3. ↑ With unchanged references, as reported by Tietz; he was not promoted because his poor clothes were considered inappropriate. According to Tietz, his lectures were very popular with students.
4. ↑ initially “Professor with a full teaching assignment”, from 1965 “Professor with a Chair” on a personal professorship
5. ↑ He was never a member of the Saxon Academy of Sciences.
6. ↑ Grötzsch “About some extreme problems of conformal mapping. I, II ”,“ About the distortion in simple non-conforming images and about a related extension of Picard's theorem ”, session reports Saxon Akad. Wiss., Math-Phys. Class, Vol. 80, 1928, pp. 367-376, 497-502, 503-507
7. ^ J. Milnor, Dynamics in one complex variable , Vieweg, Braunschweig, 1999; P. 212.