Minimal real currents on compact Riemannian manifolds
Izvestiya. Mathematics , Tome 11 (1977) no. 4, pp. 807-820.

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In this article we obtain a necessary and sufficient condition for the minimality of real currents in homology classes of a compact Riemannian manifold that are associated with forms with zero covariant derivative. This condition is used, in particular, to study the minimality of surfaces in compact Lie groups. Bibliography: 14 titles.
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Dào Trong Thi. Minimal real currents on compact Riemannian manifolds. Izvestiya. Mathematics , Tome 11 (1977) no. 4, pp. 807-820. http://geodesic.mathdoc.fr/item/IM2_1977_11_4_a5/

[1] Bombieri E., De Giorgi E., Giusti E., “Minimal cones and the Bernstein problem”, Invent. Math., 7:3 (1969), 243–268 | DOI | MR | Zbl

[2] Dynkin E. B., “Gomologii kompaktnykh grupp Li”, Uspekhi matem. nauk, VIII:5 (1953), 73–120 | MR

[3] Kartan E., Geometriya grupp Li i simmetricheskie prostranstva, IL, M., 1949

[4] Cartan E., “La théorie des groupes finis et continus et l'analysis situs”, Mem. Sci. Math., XLII (1930)

[5] Lawson H. B., “The stable homology of a flat torus”, Math. Scand., 36:1 (1975), 49–73 | MR | Zbl

[6] Lawson H. B., “The equivariant Plateau problem and interior regularity”, Trans. Amer. Math. Soc., 173 (1972), 231–249 | DOI | MR | Zbl

[7] Likhnerovich A., Teoriya svyaznostei v tselom i gruppy golonomii, IL, M., 1960

[8] Pontryagin L. S., “Homologies in compact Lie groups”, Matem. sb., 6(48) (1938), 389–422

[9] Rashevskii P. K., “O veschestvennykh kogomologiyakh odnorodnykh prostranstv”, Uspekhi matem. nauk, XXIV:3 (1969), 23–90

[10] Federer H., Geometric measure theory, 153, Springer, Berlin, 1969 | MR | Zbl

[11] Federer H., Fleming W. H., “Normal and integral currents”, Ann. Math., 72:3 (1960), 458–520 | DOI | MR | Zbl

[12] Federer H., “Some theorems on integral currents”, Trans. Amer. Math. Soc., 117:5 (1965), 43–67 | DOI | MR | Zbl

[13] Fomenko A. T., “Vpolne geodezicheskie modeli tsiklov”, Tr. seminara po vekt. i tenz. analizu, 16, 1972, 14–98 | MR | Zbl

[14] Fomenko A. T., “Minimalnye kompakty v rimanovykh mnogoobraziyakh i gipoteza Raifenberga”, Izv. AN SSSR. Ser. matem., 36 (1972), 1049–1079 | MR | Zbl