• [1] P. Alexandroff and H. Hopf, Topologie, Berlin, 1935.
• [2] S. Banach, Théorie des opérations linéaires, Warsaw, 1932.
• [3] L. Cesari, An existence theorem in the calculus of variations for integrals on parametric surfaces, Amer. J. Math. vol. 74 (1952) pp. 265-295. MR 0050187 (14:292b)
• [4] W. Damköhler, Über indefinite Variationsprobleme, Math. Ann. vol. 110 (1935) pp. 230-283. MR 1512938
• [5] W. Damköhler and E. Hopf, Über einige Eigenschaften von Kurvenintegralen und über die Aequivalenz von indefiniten mit definilen Variationsproblemen, Math. Ann. vol. 120 (1947-49) pp. 12-20. MR 0022660 (9:242e)
• [6] J. M. Danskin, On the existence of minimizing surfaces in parametric double integral problems in the calculus of variations, Rivista Mat. Parma vol. 3 (1952) pp. 43-63. MR 0050186 (14:292a)
• [7] W. V. D. Hodge, The theory and applications of harmonic integrals, Cambridge, 1941. MR 0051571 (14:500b)
• [8] M. Krein and D. Milman, On extreme points of regularly convex sets, Studia Math. vol. 9 (1940) pp. 133-138. MR 0004990 (3:90a)
• [9] S. Lefschetz, Algebraic topology, Amer. Math. Soc. Colloquium Publications, vol. 27, 1942. MR 0007093 (4:84f)
• [10] E. J. McShane, Generalized curves, Duke Math. J. vol. 6 (1940) pp. 513-536. MR 0002469 (2:59d)
• [11] D. Milman, Characteristics of extremal points of regularly convex sets, Doklady Akad. Nauk SSSR. N.S. vol. 57 (1947) pp. 119-122. MR 0022313 (9:192d)
• [12] S. Saks, Theory of the integral, Warsaw, 1937.
• [13] A. G. Sigalov, Two dimensional problems in the calculus of variations, Uspehi Mat. Nauk N.S. vol. 6 (1951) pp. 16-101. MR 0043400 (13:257d)
• [14] L. C. Young, Generalized curves and the existence of an attained absolute minimum in the calculus of variations, Comptes Rendus de la Société des Sciences et des Lettres de Varsovie, Classe III, vol. 30 (1937) pp. 212-234.
• [15] -, Generalized surfaces in the calculus of variations, Ann. of Math. vol. 43 (1942) pp. 84-103. MR 0006023 (3:249a)
• [16] -, Generalized surfaces in the calculus of variations. II, Ann. of Math. vol. 43 (1942) pp. 530-544. MR 0006832 (4:49d)
• [17] -, Some applications of the Dirichlet integral to the theory of surfaces, Trans. Amer. Math. Soc. vol. 64 (1948) pp. 317-335. MR 0026118 (10:109d)
• [18] -, Surfaces paramétriques généralisées, Bull. Soc. Math. France vol. 79 (1951) pp. 59-85.

Bibliography

[1]

P. Alexandroff and H. Hopf, Topologie, Berlin, 1935.

[2]

S. Banach, Théorie des opérations linéaires, Warsaw, 1932.

[3]

L. Cesari, An existence theorem in the calculus of variations for integrals on parametric surfaces, Amer. J. Math. vol. 74 (1952) pp. 265-295. MR 0050187 (14:292b)

[4]

W. Damköhler, Über indefinite Variationsprobleme, Math. Ann. vol. 110 (1935) pp. 230-283. MR 1512938

[5]

W. Damköhler and E. Hopf, Über einige Eigenschaften von Kurvenintegralen und über die Aequivalenz von indefiniten mit definilen Variationsproblemen, Math. Ann. vol. 120 (1947-49) pp. 12-20. MR 0022660 (9:242e)

[6]

J. M. Danskin, On the existence of minimizing surfaces in parametric double integral problems in the calculus of variations, Rivista Mat. Parma vol. 3 (1952) pp. 43-63. MR 0050186 (14:292a)

[7]

W. V. D. Hodge, The theory and applications of harmonic integrals, Cambridge, 1941. MR 0051571 (14:500b)

[8]

M. Krein and D. Milman, On extreme points of regularly convex sets, Studia Math. vol. 9 (1940) pp. 133-138. MR 0004990 (3:90a)

[9]

S. Lefschetz, Algebraic topology, Amer. Math. Soc. Colloquium Publications, vol. 27, 1942. MR 0007093 (4:84f)

[10]

E. J. McShane, Generalized curves, Duke Math. J. vol. 6 (1940) pp. 513-536. MR 0002469 (2:59d)

[11]

D. Milman, Characteristics of extremal points of regularly convex sets, Doklady Akad. Nauk SSSR. N.S. vol. 57 (1947) pp. 119-122. MR 0022313 (9:192d)

[12]

S. Saks, Theory of the integral, Warsaw, 1937.

[13]

A. G. Sigalov, Two dimensional problems in the calculus of variations, Uspehi Mat. Nauk N.S. vol. 6 (1951) pp. 16-101. MR 0043400 (13:257d)

[14]

L. C. Young, Generalized curves and the existence of an attained absolute minimum in the calculus of variations, Comptes Rendus de la Société des Sciences et des Lettres de Varsovie, Classe III, vol. 30 (1937) pp. 212-234.

[15]

-, Generalized surfaces in the calculus of variations, Ann. of Math. vol. 43 (1942) pp. 84-103. MR 0006023 (3:249a)

[16]

-, Generalized surfaces in the calculus of variations. II, Ann. of Math. vol. 43 (1942) pp. 530-544. MR 0006832 (4:49d)

[17]

-, Some applications of the Dirichlet integral to the theory of surfaces, Trans. Amer. Math. Soc. vol. 64 (1948) pp. 317-335. MR 0026118 (10:109d)

[18]

-, Surfaces paramétriques généralisées, Bull. Soc. Math. France vol. 79 (1951) pp. 59-85.