Werner Fenchel

Fenchel was born on 3 May 1905 in Berlin, Germany,{{cite web|title=Theseus Curriculum Vitae of Werner Fenchel|url=http://www.math.ku.dk/ths/fenchel_w/|work=Theseus|access-date=28 December 2012}} his younger brother was the Israeli film director and architect Heinz Fenchel.

Fenchel studied mathematics and physics at the University of Berlin between 1923 and 1928. He wrote his doctorate thesis in geometry (Über Krümmung und Windung geschlossener Raumkurven){{cite web|title=Virtual Internet Authority File 2603673|url=http://viaf.org/viaf/2603673/|access-date=28 December 2012}} under Ludwig Bieberbach.

From 1928 to 1933, Fenchel was Professor E. Landau's Assistant at the University of Göttingen. During a one-year leave (on Rockefeller Fellowship) between 1930 and 1931, Fenchel spent time in Rome with Tullio Levi-Civita, as well as in Copenhagen with Harald Bohr and Tommy Bonnesen.

He visited Denmark again in 1932.

Fenchel taught at Göttingen until 1933, when the Nazi discrimination laws led to mass-firings of Jews.{{cite journal|last=Kiselman|first=Christer|title=Werner Fenchel: A pioneer in convexity theory|pages=133–152|year=2019|journal=Göteborg: Nationellt centrum för matematikutbildning (NCM)|volume=61|issue=2–4|url=http://www.cb.uu.se/~kiselman/fenchel.pdf|quote=Many scientists in Germany lost their jobs after the Nazi Machtübernahme in 1933. Fenchel was one of them. It seems appropriate to describe in some detail this development, which is of interest also because of the general decline of science and culture in Germany. See also Gordin (2015: Chapter 7, Unspeakable)}}

Fenchel emigrated to Denmark somewhere between April and September 1933, ultimately obtaining a position at the University of Copenhagen. In December 1933, Fenchel married fellow German refugee mathematician Käte Sperling.

When Germany occupied Denmark, Fenchel and roughly eight-thousand other Danish Jews received refuge in Sweden, where he taught (between 1943 and 1945) at the Danish School in Lund. After the Allied powers' liberation of Denmark, Fenchel returned to Copenhagen.

In 1946, Fenchel was elected a member of the Royal Danish Academy of Sciences and Letters.

On leave between 1949 and 1951, Fenchel taught in the U.S. at the University of Southern California, Stanford University, and Princeton University.

From 1952 to 1956 Fenchel was the professor in mechanics at the Polytechnic in Copenhagen.

From 1956 to 1974 he was the professor in mathematics at the University of Copenhagen.

Professor Fenchel died on 24 January 1988.

{{main|Convex geometry}}

{{see also|Alexandrov–Fenchel inequality}}

{{main|Convex analysis}}

{{see also|Convex set|Convex cone|Convex function}}

{{see also|Legendre-Fenchel transformation|Fenchel's duality theorem}}

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.

{{main|Hyperbolic geometry}}

{{refbegin}}

• {{cite book

| last=Fenchel

| first=Werner

|author2=Bonnesen, Tommy

| title=Theorie der konvexen Körper

| series=Ergebnisse der Mathematik und ihrer Grenzgebiete

| volume=3

| publisher=1. Verlag von Julius Springer

| location=Berlin

| year=1934

}}

• {{cite book

| last=Fenchel

| first=Werner

| title=Convex Cones, Sets, and Functions

| publisher=Princeton University Dept. of Mathematics

| location=Princeton, New Jersey

| year=1953

| url=http://rasmusen.org/x/abros/fenchel.pdf

}}

• {{cite book

| last=Fenchel

| first=Werner

|author2=Bonnesen, Tommy

| title=Theorie der konvexen Körper

| publisher=Chelsea Publishing Co.

| location=Bronx, New York

| others= (Reprint of the 1948 German language edition)

| year=1971

}}

• {{cite book

| last=Fenchel

| first=Werner

|author2=Bonnesen, Tommy

| title=Theorie der konvexen Körper

| publisher=Springer-Verlag

| location=Berlin-New York

| year=1974

}}

• {{cite book

| last=Fenchel

| first=Werner

|author2=Bonnesen, Tommy

| title=Theory of convex bodies

| url=https://archive.org/details/theoryofconvexbo0000bonn

| url-access=registration

| publisher=L. Boron, C. Christenson and B. Smith. BCS Associates

| location=Moscow, Idaho

| year=1987

| isbn=9780914351023

}}

• {{cite book

| last=Fenchel

| first=Werner

| title=Elementary geometry in hyperbolic space

| series=De Gruyter Studies in mathematics

| volume=11

| publisher=Walter de Gruyter & Co.

| location=Berlin-New York

| year=1989

}}

• {{cite book

| last1=Fenchel

| first1=Werner

| last2=Nielsen

| first2= Jakob

| author2-link=Jakob Nielsen (mathematician)

| editor-last=Schmidt

| editor-first=Asmus L.

| title=Discontinuous groups of isometries in the hyperbolic plane

| series=De Gruyter Studies in mathematics

| volume=29

| publisher=Walter de Gruyter & Co.

| location=Berlin

| year=2003

}}

{{refend}}

{{div col|colwidth=22em}}

• Convex analysis
• Convex cone
• Convex function
• Convex set
• Legendre–Fenchel transformation
• Convex minimization
• Fenchel's duality theorem
• Geometry
• Convex geometry
• Brunn–Minkowski theorem
• Differential geometry
• Fenchel's theorem
• Hyperbolic geometry
• Jakob Nielsen
• Fenchel–Nielsen coordinates
• Nonlinear programming

{{div col end}}

{{reflist}}

• {{MathGenealogy|id=19720}}
• [http://www.math.ku.dk/ths/fenchel_w/ Werner Fenchel website] – contains CV, biography, links to archive, etc.

{{Authority control}}

{{DEFAULTSORT:Fenchel, Werner}}

Category:Geometers

Category:Differential geometers

Category:20th-century German mathematicians

Category:Danish mathematicians

Category:Jewish emigrants from Nazi Germany to Denmark

Category:1905 births

Category:1988 deaths

Category:Variational analysts