INSTITUTE FOR MATHEMATICAL SCIENCES|
UNIVERSITY OF COPENHAGEN
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There are reprints of the following book reviews and solutions of problems:
General, short description of the collection
A short biography of Werner Fenchel
Werner Fenchel (1905-88) was born in Berlin. He studied physics and mathematics
at the University of Berlin, and he decided to concentrate on mathematics.
In 1928 he submitted his doctoral dissertation
about closed space curves. His first academic position was as an assistant
to professor E. Landau at the University of Göttingen.
During the years 1930-32 he went abroad several times on a Rockefeller
fellowship. He stayed in Italy
and he also went to Denmark for a period to collaborate with Bonnesen.
When the Nazis took over power in 1933 many Jews in the state administration,
including the universities, soon lost their jobs. Because Fenchel was of
Jewish descent he was also affected, and he left for Denmark. In December
1933 he married Käte Sperling, who also was a mathematical refugee. They
managed to get things going by having temporary jobs. They both felt at home
among the Danish mathematicians, and Werner Fenchel collaborated
with several of them. As most other Jews in Denmark they succeeded in
escaping to Sweden during 1943-45. During that period they were both teaching
at the Danish School in Lund. In 1947 Fenchel got a position in mathematics
at the Technical University. He became professor in rational mechanics
the same place in 1951 and in 1956 he succeeded Nørlund as professor
in mathematics at the University of Copenhagen. Fenchel's scientific work
was mainly in two subjects. In the early period he worked on the theory of
convexity, while in his later years, after World War II, he worked on a
theory of discontinuous groups of motion in the non-Euclidean plane.
He was involved in the publication of the collected works of Jakob Nielsen.
A survey of the content of the collection
THe Werner Fenchel papers have been divided into subjects and the material
belonging to a subject has then, as far as possible, been sorted
chronologically. Unfortunately, a lot of the material is undated and for
a major part of the manuscripts it has not been possible to decide whether
it was the manuscript for a lecture or a draft for a scientific work.
Hence the division into "scientific manuscripts" and "manuscripts for
lectures" is not very sharp, i.e. one may find manuscripts for lectures
in the subject "scientific manuscripts".
Biographical material and correspondence
Manuscripts for lectures
Material concerning Jakob Nielsen
List of the content of each of the boxes
BIOGRAPHICAL MATERIAL AND CORRESPONDENCE
Folder: Press clippings
Folder: His 70th anniversary
Folder: Correspondence from Jakob Nielsen 1939-59
Folder: Miscellaneous correspondence
Folder: Konvexität und Dualität [>1976]
Folder: Manuscripts on convex sets and functions
Folder: Manuscript on homology and cohomology
Folder: Riemannsk geometri [Riemannian geometry]
Envelope: Überlagungsfläche und Fundamentalgruppe
Sections of a book manuscript on "Discontinuous groups and motions", 1
Envelope: W. Fenchel: Introduzione alla teoria dei gruppidiscontinui di trasformazioni
W. Fenchel: Introduzione alla teoria dei gruppi discontinui di trasformazioni 1956
Folder: Miscellaneous manuscripts
MANUSCRIPTS FOR LECTURES
Plastic folder: Diskontinuerte transformationsgrupper
Plastic folder: W. Fenchel: On trigonometry in hyperbolic 3-space
Plastic folder: Über diskontinuierliche Isometriegruppen der nicht-euklidischen Ebene und ein Problem der Flächentopologie
Plastic folder: Transparencies in German (8 pieces).
Plastic folder: Transparencies in German for non-Euclidean Geometry (12 pieces).
Folder: Lecture on topology of surfaces
Folder: Manuscripts for lectures 1940-1963
Folder: Notes and manuscripts for lectures on topology 1954-56
Folder: Manuscript for lecture: Ikke-euklidisk geometri 1964.
W. Fenchel: Convex Bodies 1951
W. Fenchel: Convex cones, sets, and functions 1951 (3 copies)
W. Fenchel: Om differential- og integralregningens opbygning 1956
W. Fenchel: Conjugate convex functions 1964 (5 copies)
Seminar over konvekse mængder og funktioner 1965
Folder: Notes on topology and groups
Folder: Reprint of articles 1929-47
Folder: Reprint of articles 1948-83 etc.
Folder: Encyclopedia articles
T. Bonnesen und W. Fenchel: Theorie der Konvexen Körper 1934 (2 copies)
MATERIAL CONCERNING JAKOB NIELSEN
Folder: Jakob Nielsen's collected works
Manuscript: Vagn Lundsgaard Hansen: En dansk matematikers eventyr
Obituary of Jakob Nielsen
Folder: Jakob Nielsen reprints
Georg Hajós: Über einfache und mehrfache Bedeckung des n- dimensionalen Raumes mit einem Würfelgitter. Photocopy of pp. 427-67 of a journal from 1941.
Ladislaus Rédei: Neuer Beweis des Hajósschen Satzes über die endlichen Abelschen Gruppen. Photocopy of pp. 27-39 of a journal.
L. Rédei: Die neue Theorie der Endlichen Abelschen Gruppen und Verallgemeinerung des Hauptsatzes von Hajós. Photocopy of pp. 329-373 of a journal.
John Stillwell: Poincaré, Dehn, and the Origins of Nielsen's Theory of Surfaces. Typewritten manuscript, 38 pp.
John C. Stillwell: Translation of Dehn's 1922 Breslau Lecture. Paper No. 1, October 1981. Department of Mathematics, Monash University, Australia.
Vagn Lundsgaard Hansen: En geometer ser på naturen. Photocopy of typewritten manuscript, 24 pp.
Allan Sandqvist: En forbindelse mellem sædvanlige ikke-lineære differentialligninger af 1. orden og variationsregning. Mat-report No. 1986-05, Matematisk Institut, Danmarks Tekniske Højskole, Februar 1986.
Norbert Schappacher: Das Mathematische Institut der Universität Göttingen 1929-1950. Typewritten, in German, 43 pp.
Menniche m.fl.: Typewritten notes on among other things Folder: Miscellaneous
Details about the content of some of the folders
Letters in English from Donald W. Blackett, Harold Kuhn and A. W. Tucker from the period 1951-53. The letters are mainly about proof-reading of Fenchel's lecture notes. Furthermore, there is the carbon copy of a letter from Fenchel to Kuhn. There are 2 letters from Blackett, 2 from Kuhn and 11 from Tucker.
Carbon copies of 2 letters in English from W. Fenchel to Gerstenhaber from 1954 concerning Fenchel's review of a work by Gerstenhaber (the review is also included), and a letter in English from Gerstenhaber to Wehausen from 1954 on the same subject.
A postcard in German from Otto Haupt to W. and K. Fenchel from 1967.
A letter in German from Annemarie Ulm to W. and K. Fenchel from 1983.
A letter from Vagn Lundsgaard Hansen to W. Fenchel from 1982.
Two handwritten manuscripts in German in Fenchel's handwriting without title, date and author. Each is 5 pages long.
Duality in the theory of convex functions. Handwritten manuscript in English in Fenchel's handwriting without date and author. 20 pp.
Two handwritten manuscripts in English in Fenchel's handwriting without title, date and author. They are respectively 5 and 3 pages long.
A simple solution of the isoperimetric problem. Handwritten manuscript in English in Fenchel's handwriting without author and date.
Det isoperimetriske problem [The isoperimetic problem]. Handwritten manuscript in Danish in Fenchel's handwriting without author, or date. 9 pp.
Handwritten manuscript in Danish in Fenchel's handwriting on convex sets without title, author and date. 6 pp.
Kap. VIII. Konvekse Funktioner [Convex functions]. Handwritten draft for a manuscriptin Danish in Fenchel's handwriting. There are 39 numbered pages followed by 19 numbers pages entitled: Kap. N+1: Støttefunktion [Support function] and Kap. N+2: Polaritet[Polarity], a chapter about volume determination on 13 numbered pages, a chapter entitled Tschebyscheff-Approximationen on 7 numbered pages and, finally, a chapter on n dimensional spaces on 19 pages.
Paragraf 2. Fundamentalgruppe [The fundamental group].
Paragraf 2. Overlejringsrum.
H-rum [H spaces].
Numerabel basis [Countable basis].
Deling af enheden [Division of the unit].
Vektorfelter [Vector fields].
Riemann mangfoldigheder [Riemann manifolds].
Differentialformer [Differential forms].
Singulær homologi [Singular homology].
Stokes' sætning [Stokes' theorem].
Differentiabel singulær homologi [Differentiable singular homology].
G. de Rham cohomologi [G. de Rham cohomology].
Riemann flader [Riemann surfaces].
Hilbertrummet af differentialformer [The Hilbert space of differential forms].
Lectures by A. W. Tucker: Topology. Summer Conference for High School Teachers of Mathematics, University of Washington, Seattle, July 26 - August 20, 1954. Fenchel's copy of typewritten stencils (38 pages long with 19 pages of exercises) divided into the following sections:
Lecture 2: The Topological Anatomy of Surfaces (Notes by Richard Long, pp. 4-12)
Lecture 3: Continuous Mappings and Vector Fields (Notes by Robert Ives, pp. 13-18)
Lecture 4: Continuous Mappings and Vector Fields (Notes by Richard Long, pp. 19-28)
Lecture 5: Manifolds, Products, and Fiberings (Notes by Robert Ives, pp. 29-38)
Dr. Hopf: Vorlesungen über Topologie. 168 typewritten pages of stencils.
W. Fenchel: Convex cones, sets, and functions. From notes by D. W. Blackett of lectures at Princeton University, Spring Term 1951. September 1953. With a list of errors included in the end. (2 copies of which one has an additional list of errors).
Typewrittne and handwritten bibliography of W. Fenchel's publications with complete reference. It contains 47 works.
Three reprints of Ur Svensk Uppslagsbok with Fenchel's article on
"mathematics". Reprints of Salmonsen Leksikon-Tidsskrift issue no. 7
(1943) and issue no. 12 (1951) with articles on Hilbert respectively Harald
Bohrwritten by Fenchel.
Cirkeldelning [Division of the circle], 1 page typewritten in Danish.
Grafisk beräkning [Graphical computation], 1 page typewritten in Danish.
Hamilton, Sir William Rowan, 1 page typewritten in Danish.
Hardy, Godfrey Harold, 1 page typewritten in Danish.
Hilbert, David, 2 pages typewritten in Danish.
Matematik [Mathematics], 14 pages typewritten in Danish in 2 copies.
Mängdlära, mängdteori [Set theory], 3 pages typewritten in Danish.
Neumann, John von, 1 page typewritten in Danish.
Oändelighetsbegreppet [The concept of infinity], 3 pages typewritten in Danish.
Parallellförskjutning [Map made by parallel movement], 1 page typewritten in Danish.
Pi, 2 pages typewritten in Danish.
Projektiv geometri [Projective geometry], 2 pages typewritten in Danish.
Punkt, [Point] 1 page typewritten in Danish.
Pyramid, [Pyramid] 1 page typewritten in Danish.
Reella funktioner [Real functions], 1 page typewritten in Danish.
Rektifikation [Rectification], 1 page typewritten in Danish.
Riemann, Bernhard, 1 page typewritten in Danish.
Rum [Spaces], 2 pages typewritten in Danish.
Stereografisk projektion [Stereographical projection], 1 page typewritten in Danish.
Tidsskrifter [Journals], 3 pages typewritten in Swedish.
A photocopy of a typewritten manuscript in English that is a translation of the above mentioned lectures, because the title is: The mapping types of closed surfaces and their relationship with infinite groups (2 Lectures, given in Breslau on the 9th and 11th of March 1921, by J. Nielsen). It is 13 pages long.
There are reprints of the following book reviews and solutions of problems: