On the instability of a minimal surface in an $n$-dimensional Riemannian space of positive curvature
Sbornik. Mathematics, Tome 29 (1976) no. 3, pp. 359-375 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper the question of minimal two-dimensional surfaces in an $n$-dimensional Riemannian space (surfaces with zero mean curvature vector) is investigated. Bibliography: 24 titles.
@article{SM_1976_29_3_a4,
     author = {Yu. A. Aminov},
     title = {On the instability of a~minimal surface in an $n$-dimensional {Riemannian} space of positive curvature},
     journal = {Sbornik. Mathematics},
     pages = {359--375},
     year = {1976},
     volume = {29},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_29_3_a4/}
}
TY  - JOUR
AU  - Yu. A. Aminov
TI  - On the instability of a minimal surface in an $n$-dimensional Riemannian space of positive curvature
JO  - Sbornik. Mathematics
PY  - 1976
SP  - 359
EP  - 375
VL  - 29
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1976_29_3_a4/
LA  - en
ID  - SM_1976_29_3_a4
ER  - 
%0 Journal Article
%A Yu. A. Aminov
%T On the instability of a minimal surface in an $n$-dimensional Riemannian space of positive curvature
%J Sbornik. Mathematics
%D 1976
%P 359-375
%V 29
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1976_29_3_a4/
%G en
%F SM_1976_29_3_a4
Yu. A. Aminov. On the instability of a minimal surface in an $n$-dimensional Riemannian space of positive curvature. Sbornik. Mathematics, Tome 29 (1976) no. 3, pp. 359-375. http://geodesic.mathdoc.fr/item/SM_1976_29_3_a4/

[1] H. A. Schwarz, Mathematische Abhandlungen, I, 1885

[2] R. Kurant, Printsip Dirikhle, konformnye otobrazheniya i minimalnye poverkhnosti, IL, Moskva, 1953

[3] H. Federer, “Some theorems on integral currents”, Trans. Amer. Math. Soc., 11 (1965), 43–67 | DOI | MR

[4] F. G. Almgren, “Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem”, Ann. Math., 85 (1966), 277–292 | DOI | MR

[5] D. Saimons, “Minimalnye poverkhnosti v rimanovykh mnogoobraziyakh”, Matematika, 16:6 (1972), 60–104

[6] H. B. Lawson, I. Simons, “On stable currents and their application to global problems in real and complex geometry”, Ann. Math., 98 (1973), 427–450 | DOI | MR | Zbl

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

[8] A. T. Fomenko, “Periodichnost Botta s tochki zreniya mnogomernogo funktsionala Dirikhle”, Izv. AN SSSR, seriya matem., 35 (1971), 667–681 | MR | Zbl

[9] V. A. Toponogov, “Zavisimost mezhdu kriviznoi i topologicheskim stroeniem rimanovykh prostranstv chetnoi razmernosti”, DAN SSSR, 133:5 (1960), 1031–1033 | MR | Zbl

[10] W. Klingenberg, “Über Reimannsche Mannigfaltigkeiten mit positiver Krümmung”, Comm. math. Helv., 35 (1961), 35–54 | DOI | MR | Zbl

[11] M. Berger, “Les variétés riemanniennes 1/4-pinces”, Ann. Scuola Norm. Sup., Pisa, 14 (1960), 161–170 | MR | Zbl

[12] V. Blyashke, Differentsialnaya geometriya, ONTI, Moskva, 1935

[13] A. Duschek, “Zur geometrischen Variationsrechnung”, Math. Z., 40 (1936), 279–291 | DOI | MR

[14] A. Duschek, W. Mayer, Lehrbuch der Differentialgeometrie, bd. 2, Leipzig–Berlin, 1930

[15] L. P. Eizenkhart, Rimanova geometriya, IL, Moskva, 1948

[16] L. S. Pontryagin, Gladkie mnogoobraziya i ikh primeneniya v teorii gomotopii, Trudy matem. in-ta im. V. A. Steklova AN SSSR, XLV, 1955 | MR | Zbl

[17] I. N. Vekua, Obobschennye analiticheskie funktsii, Fizmatgiz, Moskva, 1959 | MR

[18] A. V. Pogorelov, Vneshnyaya geometriya vypuklykh poverkhnostei, izd-vo «Nauka», Moskva, 1969 | MR

[19] M. Berger, “Sur quelques varietes Riemanniennes suffisamment pincees”, Bull. Soc. Math. France, 88 (1960), 57–71 | MR | Zbl

[20] M. Sugimoto, K. Shiohama, “On the Differentiable Pinching Problem”, Math. Ann., 195:1 (1971), 1–16 | DOI | MR

[21] D. Milnor, “Differentsialnaya topologiya”, Uspekhi matem. nauk, XX:6 (126) (1965), 41–54 | MR

[22] S. Smale, “A classification of immersions of the two-sphere”, Trans. Amer. Math. Soc., 90 (1959), 281–292 | DOI | MR

[23] M. A. Kervaire, “Sur le fibré normal à une sphére immergée dans une espace euclidien”, Comm. math. Helv., 33:2 (1959), 121–131 | DOI | MR | Zbl

[24] Yu. A. Aminov, “K probleme ustoichivosti minimalnoi poverkhnosti v rimanovom prostranstve polozhitelnoi krivizny”, DAN SSSR, 224:4 (1975), 745–747 | MR | Zbl