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**Moritz Werner Fenchel**
Moritz Werner Fenchel
	; Werner Fenchel, 1972
Born	May 3, 1905; Berlin, Germany
Died	January 24, 1988 (aged 82);
Residence	Germany,Denmark,USA
Citizenship	German
Ethnicity	Jewish
Fields	Mathematics:; Geometry; Optimization
Institutions	University of Copenhagen; University of Göttingen
Alma mater	University of Berlin
Doctoral advisor	Ludwig Bieberbach
Doctoral students	Birgit Grodal
Known for	Convex analysis; Legendre–Fenchel transformation; Fenchel's duality theorem
Influenced	Victor Klee; R. T. Rockafellar

Moritz Werner Fenchel (May 3, 1905 – January 24, 1988) was a mathematician known for his contributions to geometry and to optimization theory. Fenchel established the basic results of convex analysis and nonlinear optimization theory. Fenchel's monographs and lecture-notes were very influential also. Fenchel lived most of his life in Denmark.

[edit] Geometric contributions

[edit] Convex geometry

Main article: Convex geometry

[edit] Optimization theory

Main article: Convex analysis

See also: Convex set, Convex cone, and Convex function

Fenchel lectured on "Convex Sets, Cones, and Functions" at Princeton University in the early 1950s. His lecture notes shaped the field of convex analysis, according to the monograph Convex Analysis of R. T. Rockafellar.

[edit] Hyperbolic geometry

Main article: Hyperbolic geometry

[edit] Biographical history

Fenchel was born in Germany and wrote his doctorate thesis in geometry (Über Krümmung und Windung geschlossener Raumkurven) under Ludwig Bieberbach at the University of Berlin. He then taught at the University of Göttingen, until 1933 when the Nazi discrimination laws led to mass-firings of Jews.

Fenchel fled to Denmark in 1933, and then obtained a position at the University of Copenhagen. When Germany occupied Denmark, Fenchel and roughly eight-thousand other Danish Jews received refuge in Sweden. After the liberation of Denmark, Fenchel returned to Copenhagen.

[edit] Books

Fenchel, Werner; Bonnesen, Tommy (1934). Theorie der konvexen Körper. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Berlin: 1. Verlag von Julius Springer.
Fenchel, Werner; Bonnesen, Tommy (1971). Theorie der konvexen Körper. Bronx, New York: Chelsea Publishing Co..
Fenchel, Werner; Bonnesen, Tommy (1974). Theorie der konvexen Körper. Berlin-New York: Springer-Verlag.
Fenchel, Werner; Bonnesen, Tommy (1987). Theory of convex bodies. Moscow, Idaho: L. Boron, C. Christenson and B. Smith. BCS Associates.
Fenchel, Werner (1989). Elementary geometry in hyperbolic space. De Gruyter Studies in mathematics. 11. Berlin-New York: Walter de Gruyter & Co..
Fenchel, Werner; Nielsen, Jakob; edited by Asmus L. Schmidt (2003). Discontinuous groups of isometries in the hyperbolic plane. De Gruyter Studies in mathematics. 29. Berlin: Walter de Gruyter & Co..