Person: Douglas, Jesse
Jesse Douglas worked on geometry, group theory and the calculus of variations.
Mathematical Profile (Excerpt):
- Jesse developed a love for mathematics while he was studying at high school in New York.
- It was therefore Columbia University that Douglas entered in 1916 to undertake research under the supervision of Edward Kasner.
- He took part in Kasner's seminar on differential geometry and it was there that Douglas developed a love of geometry.
- Douglas continued to undertake research in differential geometry while teaching at Columbia College from 1920 to 1926.
- Before Douglas's solution only special cases of the problem had been solved.
- In a series of papers from 1927 onwards Douglas worked towards the complete solution: Extremals and transversality of the general calculus of variations problem of the first order in space (1927), The general geometry of paths (1927-28), and A method of numerical solution of the problem of Plateau (1927-28).
- Douglas presented full details of his solution in Solution of the problem of Plateau in the Transactions of the American Mathematical Society in 1931.
- In 1930 Douglas was appointed as an assistant professor of mathematics at the Massachusetts Institute of Technology.
- After giving a complete solution to the Plateau Problem, Douglas went on to study generalisations of it.
- In 1943 Douglas was awarded the Bôcher Prize by the American Mathematical Society for his memoirs on the Plateau Problem.
- In the first of these Douglas looked at the following form of the problem: Given an aggregate GGG of kkk non-intersecting Jordan curves in nnn-space, to find a minimal surface bounded by GGG and having a prescribed genus hhh and a prescribed orientability character (one-sided or two-sided).
- In the second paper the following problem is studied by Douglas: Given a Riemann surface (or semi-surface) RRR with boundary CCC, and given in nnn-space a topological image GGG of CCC, to prove the existence of a minimal surface topologically equivalent to RRR and bounded by GGG.
- These three papers were, amazingly, not the only ones which Douglas published in 1939.
- He also published The analytic prolongation of a minimal surface across a straight line which gives a generalisation of some earlier results on minimal surfaces with a simpler proof, The higher topological form of Plateau's problem which compares the methods which Douglas used in the first two of his papers which won the Bôcher Prize, and Minimal surfaces of higher topological structure.
- Another five papers by Douglas appeared in 1940: Theorems in the inverse problem of the calculus of variations; Geometry of polygons in the complex plane; On linear polygon transformations; A converse theorem concerning the diametral locus of an algebraic curve and A new special form of the linear element of a surface.
- In 1942 Douglas published a non-technical survey of the theory of integration.
- In the 47 page text, Douglas also mentions Fourier series and transforms, Denjoy integrals and the double integrals of Riemann and of Lebesgue.
- His wife, Jessie Douglas died in 1955, the year in which Douglas was appointed professor of mathematics at the City College of New York.
Born 3 July 1897, New York, USA. Died 7 October 1965, New York, USA.
View full biography at MacTutor
Tags relevant for this person:
Prize Fields Medal, Group Theory, Origin Usa
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- @J-J-O'Connor
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References
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive
