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Douglas developed a love of geometry studying Plateau Problems. He studied differential geometry at Columbia College from 1920 to 1926. Then from 1926 to 1930 he visited Princeton, Harvard, Chicago, Paris and Göttingen.
He gave a complete solution to the Plateau problem which was first posed by Lagrange in 1760. It was studied by Riemann, Weierstrass and Schwarz. The problem is proving the existence of a surface of minimal area bounded by a contour. Before Douglas's solution only special cases had been solved. Then he went on to study generalisations of the problem.
In 1943 Douglas was awarded the Bôcher Prize by the American Mathematical Society for his memoirs on the Plateau Problem. In particular the award was for three papers all published in 1939: Green's function and the problem of Plateau published in the American Journal of Mathematics, The most general form of the problem of Plateau published in the American Journal of Mathematics and Solution of the inverse problem of the calculus of variations published in the Proceedings of the National Academy of Sciences. Douglas also worked on the calculus of variations and, in 1951, studied groups with 2 generators x,y such that every element can be expressed in the form xy, n,m integers.
References (7 books/articles)
References elsewhere in this archive:
J Douglas was awarded the Fields Medal in 1936. You can see a history of the Fields Medal and a list of the winners.
He was the Bocher Prize winner in 1943. You can see a history of the AMS Bocher Prize and a list of the winners.