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On new results in the theory of minimal surfaces. (English) Zbl 0135.21701


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[1] E. F. Beckenbach, The area and boundary of minimal surfaces, Ann. of Math. (2) 33 (1932), no. 4, 658 – 664. · Zbl 0005.26204
[2] E. F. Beckenbach and G. A. Hutchison, Meromorphic minimal surfaces, Bull. Amer. Math. Soc. 68 (1962), 519 – 522. · Zbl 0106.14603
[3] E. F. Beckenbach and Tibor Radó, Subharmonic functions and minimal surfaces, Trans. Amer. Math. Soc. 35 (1933), no. 3, 648 – 661. · JFM 59.0488.01
[4] E. F. Beckenbach and T. Radó, Subharmonic functions and surfaces of negative curvature, Trans. Amer. Math. Soc. 35 (1933), no. 3, 662 – 674. · Zbl 0007.13001
[5] Paul W. Berg, On univalent mappings by solutions of linear elliptic partial differential equations, Trans. Amer. Math. Soc. 84 (1957), 310 – 318. · Zbl 0079.29901
[6] Serge Bernstein, Sur la généralisation du problème de Dirichlet, Math. Ann. 69 (1910), no. 1, 82 – 136 (French). · JFM 41.0427.02
[7] Serge Bernstein, Sur les équations du calcul des variations, Ann. Sci. École Norm. Sup. (3) 29 (1912), 431 – 485 (French). · JFM 43.0460.01
[8] Serge Bernstein, Sur l’intégration des équations aux dérivées partielles du type elliptique, Math. Ann. 95 (1926), no. 1, 585 – 594 (French). · JFM 52.0484.01
[9] Serge Bernstein, Über ein geometrisches Theorem und seine Anwendung auf die partiellen Differentialgleichungen vom elliptischen Typus, Math. Z. 26 (1927), no. 1, 551 – 558 (German). · JFM 53.0670.01
[10] Lipman Bers, Boundary value problems for minimal surfaces with singularities at infinity, Trans. Amer. Math. Soc. 70 (1951), 465 – 491. · Zbl 0043.15902
[11] Lipman Bers, Isolated singularities of minimal surfaces, Ann. of Math. (2) 53 (1951), 364 – 386. · Zbl 0043.15901
[12] Lipman Bers, Abelian minimal surfaces, J. Analyse Math. 1 (1951), 43 – 58. · Zbl 0045.42501
[13] Lipman Bers, Non-linear elliptic equations without non-linear entire solutions, J. Rational Mech. Anal. 3 (1954), 767 – 787. · Zbl 0056.32101
[14] L. Bers, Functional-theoretical properties of solutions of partial differential equations of elliptic type, Contributions to the theory of partial differential equations, Annals of Mathematics Studies, no. 33, Princeton University Press, Princeton, N. J., 1954, pp. 69 – 94. · Zbl 0057.08602
[15] Wilhelm Blaschke and Hans Reichardt, Einführung in die Differentialgeometrie, 2te Aufl. Die Grundlehren der mathematischen Wissenschaften, Bd. 58, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960 (German). · Zbl 0091.34001
[16] Georges Bouligand, Sur quelques problèmes fonctionnels non linéaires, C. R. Acad. Sci. Paris 241 (1955), 1537 – 1539 (French). · Zbl 0067.08106
[17] Georges Bouligand, Surfaces minima et opérateurs linéaires associés, C. R. Acad. Sci. Paris 241 (1955), 1676 – 1678 (French). · Zbl 0068.15402
[18] Eugenio Calabi, Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens, Michigan Math. J. 5 (1958), 105 – 126. · Zbl 0113.30104
[19] J. W. Calkin, Functions of several variables and absolute continuity. I, Duke Math. J. 6 (1940), 170 – 186. · JFM 66.1224.03
[20] Torsten Carleman, Zur Theorie der Minimalflächen, Math. Z. 9 (1921), no. 1-2, 154 – 160 (German). · JFM 48.0590.02
[21] Lamberto Cesari, Surface area, Annals of Mathematics Studies, no. 35, Princeton University Press, Princeton, N. J., 1956. · Zbl 0683.53003
[22] Yu Why Chen, Branch points, poles and planar points of minimal surfaces in \?³, Ann. of Math. (2) 49 (1948), 790 – 806. · Zbl 0038.33102
[23] Yu Why Chen, Existence of minimal surfaces with a simple pole at infinity and condition of transversality on the surface of a cylinder, Trans. Amer. Math. Soc. 65 (1949), 331 – 347. · Zbl 0040.37401
[24] Y. W. Chen, Discontinuity and representations of minimal surface solutions, Proceedings of the conference on differential equations (dedicated to A. Weinstein), University of Maryland Book Store, College Park, Md., 1956, pp. 115 – 138.
[25] Stefan Cohn-Vossen, Kürzeste Wege und Totalkrümmung auf Flächen, Compositio Math. 2 (1935), 69 – 133 (German). · Zbl 0011.22501
[26] L. Collatz, Sätze über monotones Verhalten bei gewöhnlichen und partiellen Differentialgleichungen, Colloq. Analyse Numér. (Mons, 1961) Librairie Universitaire, Louvain, 1961, pp. 61 – 80 (German). · Zbl 0133.38201
[27] Richard Courant, Soap film experiments with minimal surfaces, Amer. Math. Monthly 47 (1940), 167 – 174. · Zbl 0024.41704
[28] R. Courant, On Plateau’s problem with free boundaries, Proc. Nat. Acad. Sci. U. S. A. 31 (1945), 242 – 246. · Zbl 0063.00986
[29] R. Courant, Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces, Interscience Publishers, Inc., New York, N.Y., 1950. Appendix by M. Schiffer. · Zbl 0040.34603
[30] R. Courant, Unsolved problems concerning least area (with experimental demonstrations), Outlines Joint Sympos. Partial Differential Equations (Novosibirsk, 1963), Acad. Sci. USSR Siberian Branch, Moscow, 1963, pp. 305 – 307.
[31] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. · Zbl 0051.28802
[32] Richard Courant and Herbert Robbins, What is mathematics?, Oxford University Press, New York, 1979. An elementary approach to ideas and methods. · Zbl 0155.00101
[33] Hans Ludwig de Vries, A remark concerning a lemma of Heinz on harmonic mappings, J. Math. Mech. 11 (1962), 469 – 471. · Zbl 0106.04904
[34] Jesse Douglas, A method of numerical solution of the problem of Plateau, Ann. of Math. (2) 29 (1927/28), no. 1-4, 180 – 188. · JFM 54.0509.02
[35] Jesse Douglas, Solution of the problem of Plateau, Trans. Amer. Math. Soc. 33 (1931), no. 1, 263 – 321. · Zbl 0001.14102
[36] Jesse Douglas, Minimal surfaces of higher topological structure, Ann. of Math. (2) 40 (1939), no. 1, 205 – 298. · Zbl 0020.37402
[37] Jesse Douglas, The most general form of the problem of Plateau, Amer. J. Math. 61 (1939), 590 – 608. · Zbl 0021.32801
[38] Werner Fenchel, Über Krümmung und Windung geschlossener Raumkurven, Math. Ann. 101 (1929), no. 1, 238 – 252 (German). · JFM 55.0394.06
[39] Robert Finn, A property of minimal surfaces, Proc. Nat. Acad. Sci. U. S. A. 39 (1953), 197 – 201. · Zbl 0051.12504
[40] Robert Finn, Isolated singularities of solutions of non-linear partial differential equations, Trans. Amer. Math. Soc. 75 (1953), 385 – 404. · Zbl 0053.39205
[41] Robert Finn, On equations of minimal surface type, Ann. of Math. (2) 60 (1954), 397 – 416. · Zbl 0058.32501
[42] Robert Finn, On a problem of type, with application to elliptic partial differential equations, J. Rational Mech. Anal. 3 (1954), 789 – 799. · Zbl 0056.30303
[43] Robert Finn, Growth properties of solutions of nonlinear elliptic equations, Comm. Pure Appl. Math. 9 (1956), 415 – 423. · Zbl 0070.32201
[44] Robert Finn, New estimates for equations of minimal surface type, Arch. Rational Mech. Anal. 14 (1963), 337 – 375. · Zbl 0133.04601
[45] Robert Finn, Remarks on my paper, ”On equations of minimal surface type”, Ann. of Math. (2) 80 (1964), 158 – 159. · Zbl 0143.14004
[46] R. Finn and R. Osserman, On the Gauss curvature of non-parametric minimal surfaces, J. Analyse Math. 12 (1964), 351 – 364. · Zbl 0122.16404
[47] Harley Flanders, On certain functions with positive definite Hessian, Ann. of Math. (2) 71 (1960), 153 – 156. · Zbl 0093.29003
[48] Wendell H. Fleming, An example in the problem of least area, Proc. Amer. Math. Soc. 7 (1956), 1063 – 1074. · Zbl 0078.13804
[49] W. H. Fleming, Nondegenerate surfaces of finite topological type, Trans. Amer. Math. Soc. 90 (1959), 323 – 335. · Zbl 0087.27201
[50] Wendell H. Fleming, On the oriented Plateau problem, Rend. Circ. Mat. Palermo (2) 11 (1962), 69 – 90. · Zbl 0107.31304
[51] Maurice Fréchet, Détermination des surfaces minima du type \?(\?)+\?(\?)=\?(\?), Rend. Circ. Mat. Palermo (2) 5 (1956), 238 – 259 (1957) (French, with Esperanto summary). · Zbl 0086.14503
[52] P. Funk, Über zweidimensionale Finslersche Räume, insbesondere über solche mit geradlinigen Extremalen und positiver konstanter Krümmung, Math. Z. 40 (1936), no. 1, 86 – 93 (German). · JFM 61.0807.02
[53] Paul Funk, Eine Kennzeichnung der zweidemensionalen elliptischen Geometrie, Österreich. Akad. Wiss. Math.-Natur. Kl. S.-B. II 172 (1963), 251 – 269 (German). · Zbl 0151.28604
[54] René Garnier, Sur le problème de Plateau pour un quadrilatère variable qui peut acquérir un point double, C. R. Acad. Sci. Paris 251 (1960), 171 – 174 (French). · Zbl 0246.53007
[55] René Garnier, Sur le problème de Plateau pour les quadrilatères gauches ayant un sommet à l’infini, C. R. Acad. Sci. Paris 254 (1962), 2260 – 2264 (French). · Zbl 0145.18104
[56] H. Graf and H. Thomas, Zur Frage des Gleichgewichts von Vierecksnetzen aus verknoteten und gespannten Fäden. II. Rückungsfadennetze mit isotroper Spannungsverteilung und rhombischer Netzstruktur auf den Scherkschen Minimalflächen und auf den Wendelschraubenflächen, Math. Z. 51 (1948), 166 – 196 (German). · Zbl 0030.07001
[57] Donald Greenspan, On approximating extremals of functionals. I. The method and examples for boundary value problems, ICC Bull. 4 (1965), 99 – 120.
[58] Alfred Haar, Über das Plateausche Problem, Math. Ann. 97 (1927), no. 1, 124 – 158 (German). · JFM 52.0710.02
[59] Alfred Haar, Über adjungierte Variationsprobleme und adjungierte Extremalflächen, Math. Ann. 100 (1928), no. 1, 481 – 502 (German). · JFM 54.0529.01
[60] Erhard Heinz, Über die Lösungen der Minimalflächengleichung, Nachr. Akad. Wiss. Göttingen. Math.-Phys. Kl. Math.-Phys.-Chem. Abt. 1952 (1952), 51 – 56 (German). · Zbl 0048.15401
[61] Erhard Heinz, Über gewisse elliptische Systeme von Differentialgleichungen zweiter Ordnung mit Anwendung auf die Monge-Ampèresche Gleichung, Math. Ann. 131 (1956), 411 – 428 (German). · Zbl 0072.31103
[62] Erhard Heinz, On certain nonlinear elliptic differential equations and univalent mappings, J. Analyse Math. 5 (1956/1957), 197 – 272. · Zbl 0085.08701
[63] Erhard Heinz, On one-to-one harmonic mappings, Pacific J. Math. 9 (1959), 101 – 105. · Zbl 0086.28204
[64] D. Hilbert and S. Cohn-Vossen, Geometry and the imagination, Chelsea Publishing Company, New York, N. Y., 1952. Translated by P. Neményi. · Zbl 0047.38806
[65] Eberhard Hopf, On S. Bernstein’s theorem on surfaces \?(\?,\?) of nonpositive curvature, Proc. Amer. Math. Soc. 1 (1950), 80 – 85. · Zbl 0039.16901
[66] Eberhard Hopf, On an inequality for minimal surfaces \?=\?(\?,\?), J. Rational Mech. Anal. 2 (1953), 519 – 522. · Zbl 0051.12601
[67] Chuan-chih Hsiung, Isoperimetric inequalities for two-dimensional Riemannian manifolds with boundary, Ann. of Math. (2) 73 (1961), 213 – 220. · Zbl 0105.16301
[68] Alfred Huber, On the isoperimetric inequality on surfaces of variable Gaussian curvature, Ann. of Math. (2) 60 (1954), 237 – 247. · Zbl 0056.15801
[69] Alfred Huber, Zur isoperimetrischen Ungleichung auf gekrümmten Flächen, Acta Math. 97 (1957), 95 – 101 (German). · Zbl 0077.35802
[70] Alfred Huber, On subharmonic functions and differential geometry in the large, Comment. Math. Helv. 32 (1957), 13 – 72. · Zbl 0080.15001
[71] H. B. Jenkins, On two-dimensional variational problems in parametric form, Arch. Rational. Mech. Anal. 8 (1961), 181 – 206. · Zbl 0143.14804
[72] H. Jenkins, On quasi-linear elliptic equations which arise from variational problems, J. Math. Mech. 10 (1961), 705 – 727. · Zbl 0145.36402
[73] Howard Jenkins, Super-solutions for quasi-linear elliptic equations, Arch. Rational Mech. Anal. 16 (1964), 402 – 410. · Zbl 0126.11102
[74] Howard Jenkins and James Serrin, Variational problems of minimal surface type. I, Arch. Rational mech. Anal. 12 (1963), 185 – 212. · Zbl 0122.39602
[75] Hans Jonas, Die Scherksche Minimalfläche als Gegenstand einer anschaulichen geometrischen Deutung des Additionstheorems für das elliptische Integral 1. Gattung, Math. Nachr. 8 (1952), 41 – 52 (German). · Zbl 0048.38902
[76] Martin Kruskal, The bridge theorem for minimal surfaces, Comm. Pure Appl. Math. 7 (1954), 297 – 316. · Zbl 0055.39602
[77] Jacqueline Lelong-Ferrand, Représentation conforme et transformations à intégrale de Dirichlet bornée, Gauthier-Villars, Paris, 1955 (French). · Zbl 0064.32204
[78] Jean Leray, Discussion d’un problème de Dirichlet, J. Math. Pures Appl. 18 (1939), 249 – 284 (French). · Zbl 0023.04502
[79] Paul Lévy, Exemples de contours pour lesquels le problème de Plateau a 3 ou 2\?+1 solutions, C. R. Acad. Sci. Paris 224 (1947), 325 – 327 (French). · Zbl 0030.03303
[80] Paul Lévy, Le problème de Plateau, Mathematica, Timişoara 23 (1948), 1 – 45 (French).
[81] Hans Lewy, A priori limitations for solutions of Monge-Ampère equations. II, Trans. Amer. Math. Soc. 41 (1937), no. 3, 365 – 374. · Zbl 0017.21101
[82] Hans Lewy, A Property of Spherical Harmonics, Amer. J. Math. 60 (1938), no. 3, 555 – 560. · Zbl 0019.11703
[83] Hans Lewy, A note on harmonic functions and a hydrodynamical application, Proc. Amer. Math. Soc. 3 (1952), 111 – 113. · Zbl 0046.41706
[84] Hans Lewy, On the boundary behavior of minimal surfaces, Proc. Nat. Acad. Sci. U. S. A. 37 (1951), 103 – 110. · Zbl 0042.15702
[85] Hans Lewy, On mimimal surfaces with partially free boundary, Comm. Pure Appl. Math. 4 (1951), 1 – 13.
[86] S. Lozinski, On subharmonic functions and their application to the theory of surfaces, Bull. Acad. Sci. URSS. Sér. Math. [Izvestia Akad. Nauk SSSR] 8 (1944), 175 – 194 (Russian, with English summary). · Zbl 0061.24102
[87] Imanuel Marx, On the classification of unstable minimal surfaces with polygonal boundaries, Comm. Pure Appl. Math. 8 (1955), 235 – 244. · Zbl 0068.35103
[88] E. J. McShane, Parametrizations of saddle surfaces, with application to the problem of plateau, Trans. Amer. Math. Soc. 35 (1933), no. 3, 716 – 733. · Zbl 0007.11902
[89] E. J. McShane, On the analytic nature of surfaces of least area, Ann. of Math. (2) 35 (1934), no. 3, 456 – 475. · Zbl 0010.06802
[90] Earl J. Mickle, Associated double integral variation problems, Duke Math. J. 9 (1942), 208 – 227. · Zbl 0063.03923
[91] Earl J. Mickle, A remark on a theorem of Serge Bernstein, Proc. Amer. Math. Soc. 1 (1950), 86 – 89. · Zbl 0039.16902
[92] J. W. Milnor, On the total curvature of knots, Ann. of Math. (2) 52 (1950), 248 – 257. · Zbl 0037.38904
[93] C. B. Morrey Jr., Functions of several variables and absolute continuity, II, Duke Math. J. 6 (1940), 187 – 215. · JFM 66.1225.01
[94] Charles B. Morrey Jr., The problem of Plateau on a Riemannian manifold, Ann. of Math. (2) 49 (1948), 807 – 851. · Zbl 0033.39601
[95] Ch. H. Müntz, Die Lösung des Plateauschen Problems über konvexen Bereichen, Math. Ann. 94 (1925), no. 1, 53 – 96 (German). · JFM 51.0545.03
[96] Ch. H. Müntz, Zum Plateauschen Problem, Math. Ann. 96 (1927), no. 1, 597 – 600 (German). · JFM 52.0712.02
[97] Rolf Nevanlinna, Eindeutige analytische Funktionen, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Bd XLVI, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1953 (German). 2te Aufl. · Zbl 0050.30302
[98] Johannes Nitsche, Über eine mit der Minimalflächengleichung zusammenhängende analytische Funktion und den Bernsteinschen Satz, Arch. Math. (Basel) 7 (1957), 417 – 419 (German). · Zbl 0079.37701
[99] Johannes C. C. Nitsche, Elementary proof of Bernstein’s theorem on minimal surfaces, Ann. of Math. (2) 66 (1957), 543 – 544. · Zbl 0079.37702
[100] Johannes C. C. Nitsche, A uniqueness theorem of Bernstein’s type for minimal surfaces in cylindrical coordinates, J. Math. Mech. 6 (1957), 859 – 864. · Zbl 0086.14504
[101] Johannes C. C. Nitsche, On harmonic mappings, Proc. Amer. Math. Soc. 9 (1958), 268 – 271. , https://doi.org/10.1090/S0002-9939-1958-0104233-9 Johannes C. C. Nitsche, On an estimate for the curvature of minimal surfaces \?=\?(\?,\?), J. Math. Mech. 7 (1958), 767 – 769. Johannes C. C. Nitsche, A remark on Enneper’s minimal surface, Amer. Math. Monthly 66 (1959), 295 – 297. · Zbl 0092.14505
[102] Johannes Nitsche, Zu einem Satze von L. Bers über die Lösungen der Minimalflächengleichung, Arch. Math. 9 (1958), 427 – 429 (German). · Zbl 0094.34403
[103] Johannes C. C. Nitsche, On harmonic mappings, Proc. Amer. Math. Soc. 9 (1958), 268 – 271. , https://doi.org/10.1090/S0002-9939-1958-0104233-9 Johannes C. C. Nitsche, On an estimate for the curvature of minimal surfaces \?=\?(\?,\?), J. Math. Mech. 7 (1958), 767 – 769. Johannes C. C. Nitsche, A remark on Enneper’s minimal surface, Amer. Math. Monthly 66 (1959), 295 – 297. · Zbl 0092.14505
[104] Johannes C. C. Nitsche, On the constant of E. Heinz, Rend. Circ. Mat. Palermo (2) 8 (1959), 178 – 181. · Zbl 0090.05401
[105] Johannes C. C. Nitsche, Ein Eindeutigkeitssatz für zweifach zusammenhängende Minimalflächen, Math. Z. 74 (1960), 289 – 292 (German). · Zbl 0133.14401
[106] Johannes C. C. Nitsche, A characterization of the catenoid, J. Math. Mech. 11 (1962), 293 – 301. · Zbl 0106.14602
[107] Johannes C. C. Nitsche, Mathematical Notes: On the Module of Doubly-Connected Regions Under Harmonic Mappings, Amer. Math. Monthly 69 (1962), no. 8, 781 – 782. · Zbl 0109.30503
[108] Johannes C. C. Nitsche, Über die Ausdehnung gewisser zweifach zusammenhängender Minimalflächen, Math. Ann. 149 (1962/1963), 144 – 149 (German). · Zbl 0109.40302
[109] Johannes C. C. Nitsche, Zum Heinzschen Lemma über harmonische Abbildungen, Arch. Math. 14 (1963), 407 – 410 (German). · Zbl 0115.29402
[110] Johannes C. C. Nitsche, A necessary criterion for the existence of certain minimal surfaces, J. Math. Mech. 13 (1964), 659 – 666. · Zbl 0168.42304
[111] Johannes C. C. Nitsche, Über ein verallgemeinertes Dirichletsches Problem für die Minimalflächengleichung und hebbare Unstetigkeiten ihrer Lösungen, Math. Ann. 158 (1965), 203 – 214 (German). · Zbl 0141.09601
[112] Johannes C. C. Nitsche, A supplement to the condition of J. Douglas, Rend. Circ. Mat. Palermo (2) 13 (1964), 192 – 198. · Zbl 0136.16702
[113] Johannes C. C. Nitsche, On differential equations of mode 2, Proc. Amer. Math. Soc. 16 (1965), 902 – 908. · Zbl 0142.08001
[114] Johannes Nitsche and Joachim Nitsche, Ein Kriterium für die Existenz nicht-linearer ganzer Lösungen elliptischer Differentialgleichungen, Arch. Math. 10 (1959), 294 – 297 (German). · Zbl 0088.07901
[115] Johannes Nitsche and Joachim Nitsche, Über reguläre Variationsprobleme, Rend. Circ. Mat. Palermo (2) 8 (1959), 346 – 353 (German). · Zbl 0100.09901
[116] Robert Osserman, Proof of a conjecture of Nirenberg, Comm. Pure Appl. Math. 12 (1959), 229 – 232. · Zbl 0086.36202
[117] Robert Osserman, Remarks on minimal surfaces, Comm. Pure Appl. Math. 12 (1959), 233 – 239. · Zbl 0086.36301
[118] Robert Osserman, An analogue of the Heinz-Hopf inequality, J. Math. Mech. 8 (1959), 383 – 385. · Zbl 0085.15904
[119] Robert Osserman, On the Gauss curvature of minimal surfaces, Trans. Amer. Math. Soc. 96 (1960), 115 – 128. · Zbl 0093.34303
[120] Robert Osserman, Minimal surfaces in the large, Comment. Math. Helv. 35 (1961), 65 – 76. · Zbl 0098.34904
[121] Robert Osserman, On complete minimal surfaces, Arch. Rational Mech. Anal. 13 (1963), 392 – 404. · Zbl 0127.38003
[122] Robert Osserman, Global properties of minimal surfaces in \?³ and \?\(^{n}\), Ann. of Math. (2) 80 (1964), 340 – 364. · Zbl 0134.38502
[123] Robert Osserman, Global properties of classical minimal surfaces, Duke Math. J. 32 (1965), 565 – 573. · Zbl 0152.19903
[124] Oskar Perron, Eine neue Behandlung der ersten Randwertaufgabe für \Delta \?=0, Math. Z. 18 (1923), no. 1, 42 – 54 (German). · JFM 49.0340.01
[125] Tibor Radó, Zu einem Satze von S. Bernstein über Minimalflächen im Großen, Math. Z. 26 (1927), no. 1, 559 – 565 (German). · JFM 53.0670.02
[126] Tibor Radó, Bemerkungen zur Arbeit von Herrn Ch. H. Müntz über das Plateausche Problem (Math. Annalen 94, S. 53 – 96), Math. Ann. 96 (1927), no. 1, 587 – 596 (German). · JFM 52.0712.01
[127] Tibor Radó, The problem of the least area and the problem of Plateau, Math. Z. 32 (1930), no. 1, 763 – 796. · JFM 56.0436.01
[128] Tibor Radó, On the problem of Plateau. Subharmonic functions, Springer-Verlag, New York-Heidelberg, 1971. Reprint. · Zbl 0211.13803
[129] Tibor Radó, Length and Area, American Mathematical Society Colloquium Publications, vol. 30, American Mathematical Society, New York, 1948.
[130] Maxwell O. Reade, A characterization of minimal surfaces in isothermic representation, Proc. Amer. Math. Soc. 2 (1951), 47 – 54. · Zbl 0043.15801
[131] R. M. Redheffer, On pairs of harmonic functions, Proc. Amer. Math. Soc. 8 (1957), 450 – 457. · Zbl 0078.28103
[132] William T. Reid, The isoperimetric inequality and associated boundary problems, J. Math. Mech. 8 (1959), 897 – 905. · Zbl 0092.10703
[133] Herbert W. Richmond, On minimal surfaces, J. London Math. Soc. 19 (1944), 229 – 241. · Zbl 0060.35907
[134] I. F. Ritter, Solution of Schwarz’ problem concerning minimal surfaces, Univ. Nac. Tucumán. Revista A. 1 (1940), 49 – 62. · Zbl 0025.33601
[135] Shigeo Sasaki, On the total curvature of a closed curve, Japan. J. Math. 29 (1959), 118 – 125. · Zbl 0133.14204
[136] Beniamino Segre, Questioni di realtà sulle forme armoniche e sulle loro hessiane. I, Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. (8) 15 (1953), 237 – 242 (Italian). · Zbl 0055.39103
[137] Beniamino Segre, Questioni di realtà sulle forme armoniche ternarie e sulle loro hessiane, Convegno Internazionale di Geometria Differenziale, Italia, 1953, Edizioni Cremonese, Roma, 1954, pp. 148 – 151 (Italian). · Zbl 0055.39103
[138] James Serrin, Dirichlet’s principle in the calculus of variations, Proc. Sympos. Pure Math., Vol. IV, American Mathematical Society, Providence, R.I, 1961, pp. 17 – 22.
[139] James Serrin, A priori estimates for solutions of the minimal surface equation, Arch. Rational Mech. Anal. 14 (1963), 376 – 383. · Zbl 0117.07304
[140] James Serrin, Local behavior of solutions of quasi-linear equations, Acta Math. 111 (1964), 247 – 302. · Zbl 0128.09101
[141] Kêichi Shibata, On the existence of a harmonic mapping, Osaka Math. J. 15 (1963), 173 – 211. · Zbl 0132.06004
[142] Max Shiffman, The Plateau problem for minimal surfaces which are relative minima, Ann. of Math. (2) 39 (1938), no. 2, 309 – 315. · Zbl 0019.12403
[143] Max Shiffman, The Plateau problem for minimal surfaces of arbitrary topological structure, Amer. J. Math. 61 (1939), 853 – 882. · Zbl 0023.13704
[144] Max Shiffman, On surfaces of stationary area bounded by two circles, or convex curves, in parallel planes, Ann. of Math. (2) 63 (1956), 77 – 90. · Zbl 0070.16803
[145] A. G. Sigalov, Two-dimensional problems of the calculus of variations, Amer. Math. Soc. Translation 1953 (1953), no. 83, 121.
[146] Masatsugu Tsuji, On a theorem of F. and M. Riesz, Proc. Imp. Acad. Tokyo 18 (1942), 172 – 175. · Zbl 0060.35906
[147] M. Tsuji, Potential theory in modern function theory, Maruzen Co., Ltd., Tokyo, 1959. · Zbl 0087.28401
[148] J. L. Ullman and C. J. Titus, An integral inequality with applications to harmonic mappings, Michigan Math. J. 10 (1963), 181 – 192. · Zbl 0111.07805
[149] Giuseppe Vaccaro, Sulle superficie d’area minima, Riv. Mat. Univ. Parma (2) 3 (1962), 139 – 168 (Italian). · Zbl 0112.36501
[150] S. E. Warschawski, On differentiability at the boundary in conformal mapping, Proc. Amer. Math. Soc. 12 (1961), 614 – 620. · Zbl 0100.28803
[151] Walter L. Wilson Jr., On discrete Dirichlet and Plateau problems, Numer. Math. 3 (1961), 359 – 373. · Zbl 0111.29903
[152] Walter Wunderlich, Beitrag zur Kenntnis der Minimalschraubflächen, Compositio Math. 10 (1952), 297 – 311 (German). · Zbl 0047.40502
[153] Walter Wunderlich, Beitrag zur Kenntnis der Minimalspiralflächen, Rend. Mat. e Appl. (5) 14 (1954), 1 – 15 (German). · Zbl 0056.40304
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