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About the cover: The work of Jesse Douglas on minimal surfaces


Authors: Jeremy Gray and Mario Micallef
Journal: Bull. Amer. Math. Soc. 45 (2008), 293-302
MSC (2000): Primary 01A60, 53A10, 58E12
DOI: https://doi.org/10.1090/S0273-0979-08-01192-0
Published electronically: February 14, 2008
MathSciNet review: 2383307
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  • 1. Douglas, J., 1931a, Solution of the Problem of Plateau, Transactions of the American Mathematical Society 33, 263-321. MR 1501590
  • 2. Douglas, J., 1931b, The Problem of Plateau for Two Contours, Journal of Mathematics and Physics 10, 315-359.
  • 3. Douglas, J., 1939, Minimal surfaces of higher topological structure, Annals of Mathematics 40, 205-298. MR 1503457
    \begin{extrabibtext} \textbf{Abstracts of papers published by Jesse Douglas} Al... ...atical Society} and take the form year, page, article number. \end{extrabibtext}
  • 4. (1927, 143-4, 32) Reduction of the problem of Plateau to an integral equation.
  • 5. (1927, 259, 5) Reduction to integral equations of the problem of Plateau for the case of two contours.
  • 6. (1928, 405, 5) Reduction of the problem of Plateau to the minimization of a certain functional.
    \begin{extrabibtext} \textbf{Other authors} \end{extrabibtext}
  • 7. Courant, R., 1940, The existence of minimal surfaces of given topological structure under prescribed boundary conditions, Acta Mathematica 72, 51-98. MR 0002478 (2:61a)
  • 8. Garnier, R., 1928, Le Problème de Plateau, Annales Scientifiques de l'École Normale Supérieure (3) 45, 53-144. MR 1509285
  • 9. Gray, J.J., and Micallef, M.J., Minimal surfaces and the work of Jesse Douglas, book, in preparation.
  • 10. Hildebrandt, S., and von der Mosel, H., 1999, On two-dimensional parametric variational problems, Calculus of Variations and Partial Differential Equations 9 (3), 249-267. MR 1725204 (2000h:49006)
  • 11. Jost, J., 1985, Conformal mappings and the Plateau-Douglas problem in Riemannian manifolds, Journal für die reine und angewandte Mathematik 359, 37-54. MR 794798 (87d:58049)
  • 12. Koebe, P., 1917, Abhandlungen zur Theorie der konformen Abbildung, III Der allgemeine Fundamentalsatz der konformen Abbildung nebst einer Anwendung auf die konforme Abbildung der Oberfläche einer körperlichen Ecke, Journal für die reine und angewandte Mathematik 147, 67-104.
  • 13. Koebe, P., 1927, Allgemeine Theorie der Riemannschen Mannigfaltigkeiten (Konforme Abbildung und Uniformisierung) (Preisschrift), Acta Mathematica 50, 27-157. MR 1555254
  • 14. Morgan, F., 1982, On the singular structure of two-dimensional area minimizing surfaces in $ R^n$, Math. Ann. 261 (1), 101-110. MR 675210 (84c:49043)
  • 15. Morrey, C.B., Jr., 1948, The problem of Plateau on a Riemannian manifold, Annals of Mathematics 49 (4), 807-851. MR 0027137 (10:259f)
  • 16. Radó, T., 1930a, Some remarks on the problem of Plateau, Proceedings of the National Academy of Sciences 16, 242-248.
  • 17. Radó, T., 1930b, On Plateau's problem, Annals of Mathematics (2) 31, 457-69. MR 1502955
  • 18. Radó, T., 1930c, The problem of the least area and the problem of Plateau, Mathematische Zeitschrift 32, 763-96. MR 1545197
  • 19. Sacks, J., and Uhlenbeck, K., 1981, The existence of minimal immersions of $ 2$-spheres, Annals of Mathematics (2) 113, 1-24. MR 604040 (82f:58035)
  • 20. Schoen, R., and Yau, S.-T., 1979, Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature, Annals of Mathematics (2) 110, 127-142. MR 541332 (81k:58029)
  • 21. Tomi, F., and Tromba, A.J., 1988, Existence theorems for minimal surfaces of non-zero genus spanning a contour, Memoirs of the American Mathematical Society, Vol. 71, Number 382. MR 920962 (90a:58032)

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Additional Information

Jeremy Gray
Affiliation: (Gray) Centre for the History of the Mathematical Sciences, Open University, Milton Keynes, MK7 6AA, U.K.

Mario Micallef
Affiliation: (Micallef) Mathematics Institute, University of Warwick, Coventry, CV4 7AL, U.K.

DOI: https://doi.org/10.1090/S0273-0979-08-01192-0
Received by editor(s): June 11, 2007
Received by editor(s) in revised form: August 20, 2007
Published electronically: February 14, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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