Desarrollo histórico del problema de Plateau

Referencias

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[D1] DOUGLAS, J., Solution of the problem of Plateau. Transactions of the American Mathematical Society, 33 (1931), 263–321. [D2] DOUGLAS, J., The problem of Plateau. Bulletin of the American Mathematical Society, 39 (1933), 227–251. [D3] DOUGLAS, J., The problem of Plateau for two contours. Journal of Mathematics and Physics of the Massachusetts Institute of Technology, 10 (1931), 315–359. [D4] DOUGLAS, J., One–side minimal surfaces with a given boundary. Transactions of the American Mathematical Society, 34 (1932), 731–756. [D5] DOUGLAS, J., Minimal surfaces of higer topological structure. Annals of Mathematics, 40 (1939), 315–359. [FF] FEDERER, H.; FLEMING,W. H., Normal and integral currents. Annals of Mathematics, 72 (1960), 458–520. [Ga] GARNIER, R., Le probléme de Plateau. Annales Scientifiques de l’Ecole Normale Sup´erieure, 45 (1928), 53–144. [GHS] GUILLEMIN V.; KOSTANT B.; STERNBERG S., Douglas’ solution of the Plateau problem. Proceedings of the National Academy of Sciences of United States of America, 85 (1988), 3277-3278. [Gu] GULLIVER, R. D., Regularity of minimizing surfaces of prescribed mean curvature. Annals of Mathematics, 97 (1973), 275–305. [Ha] HAAR, A., Ueber das Plateausche–Problem. Mathematische Annalen, 97 (1927), 124– 158. [H1] HILDEBRANDT, S., Boundary behaviour of minimal surfaces, Archive for Rational Mechanics and Analysis, 35 (1969), 47–82. [H2] HILDEBRANDT, S., On the Plateau problem for surfaces of constant mean curvature. Communications on Pure and Applied Mathematics, 23 (1970), 97–114. [HT] HILDEBRANDT, S.; TROMBA, A., Matemáticas y formas ´optimas, Barcelona: Prensa Científica, 1990. [La] LAGRANGE, J. L., Essai d’une nouvelle méthode pour déterminer les maxima et minima des formules intégrales indéfinies. Miscellanea Taurinensia, 2 (1760), 173–195. Oeuvres de Lagrange. Paris: Gauthiers–Villars, 1, 1867, pág. 335. [Le] LEWY, H., On the boundary behaviour of minimal surfaces. Proceedings of the National Academy of Sciences of United States of America, 37 (1951), 103–110. [McS] McSHANE, E. J., Parametrizations of saddle surfaces, with applications to the problem of Plateau. Transactions of the American Mathematical Society, 35 (1933), 716–733. [Mo] MORREY, C. B., Jr., The problem of Plateau on a Riemannian manifold. Annals of Mathematics, 49 (1948), 807–851. [N1] NITSCHE J. C. C., A new uniqueness theorem for minimal surfaces. Archive for Rational Mechanics and Analysis, 52 (1973), 319–329. [N2] NITSCHE J. C. C., Minimal surfaces and partial differential equations. Editado por: LITTMAN, W., Studies in partial differential equations. Published and distributed by The Mathematical Association of America, Studies in Mathematics, Vol. 23, 1982, pp. 69–142. [Os] OSSERMAN, R., A proof of the regularity everywhere of the classical solution to Plateau’s problem. Annals of Mathematics, 91 (1970), 550–569. [Pl] PLATEAU, J. A. F., Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires. París: Gauthier–Villars, 1873. [R1] RAD´ O, T., The problem of least area and the problem of Plateau. Mathematische Zeitschrift, 32 (1930), 762–796. [R2] RAD´ O, T.,An iterative process in the problem of Plateau. Transactions of the American Mathematical Society, 35 (1933), 869–887. [R3] RAD´ O, T., On the problem of Plateau. New York: Chelsea Publishing Company, 1951. [Re] REIFENBERG, E. R., Solution of the Plateau’s problem for m–dimensional surfaces of varying topological type. Acta Mathematica, 104 (1960), 1–92. [Ri] RIEMANN, B., ¨ Uber die Fl¨ache vom Kleinsten Inhalt bei gegebener Begrenzung. Memorias de la Real Sociedad de G¨ottingen, 13, Editadas por K. Hattendorff, 1867. [Sc] SCHWARZ, H., Gesammelte Mathematische Abhandlungen. Berl´ın: Springer, 1, 1890. [Tr] TROMBA, A., On the number of solutions to Plateau’s problem. Bulletin of the American Mathematical Society, 82 (1976), 66–68. [We] WEIERSTRASS, K., Analytische Bestimmung einfach zusammenh angender Minimalfl achen deren Begrenzung aus geradliningen, ganz im endlinchen liegenden Strecken besteht. Mathematische Werke. Berlín: Mayer & Müller, 3 (1903), págs.: 39–52, 219–220, 221–238.