Geodesic
Critical points of the multidimensional Dirichlet functional
Sbornik. Mathematics, Tome 52 (1985) no. 1, pp. 141-153 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The question of the existence of local minima is considered for the Dirichlet (energy) functional on spaces of mappings of one Riemannian manifold into another. In particular, it is shown that if the identity mapping of a compact irreducible homogeneous space onto itself has positive index, then any nonconstant harmonic mapping of an arbitrary compact orientable Riemannian manifold into such a space also has positive index. Bibliography: 15 titles. 
@article{SM_1985_52_1_a8,
     author = {A. V. Tyrin},
     title = {Critical points of the multidimensional {Dirichlet} functional},
     journal = {Sbornik. Mathematics},
     pages = {141--153},
     year = {1985},
     volume = {52},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1985_52_1_a8/}
}
TY  - JOUR
AU  - A. V. Tyrin
TI  - Critical points of the multidimensional Dirichlet functional
JO  - Sbornik. Mathematics
PY  - 1985
SP  - 141
EP  - 153
VL  - 52
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1985_52_1_a8/
LA  - en
ID  - SM_1985_52_1_a8
ER  - 
%0 Journal Article
%A A. V. Tyrin
%T Critical points of the multidimensional Dirichlet functional
%J Sbornik. Mathematics
%D 1985
%P 141-153
%V 52
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1985_52_1_a8/
%G en
%F SM_1985_52_1_a8
A. V. Tyrin. Critical points of the multidimensional Dirichlet functional. Sbornik. Mathematics, Tome 52 (1985) no. 1, pp. 141-153. http://geodesic.mathdoc.fr/item/SM_1985_52_1_a8/

[1] Eells J., Lemaire L., “A report on harmonic maps”, Bull. London Math. Soc., 10:1 (1978), 1–68 | DOI | MR | Zbl

[2] Eells J., Sampson J. H., “Harmonic mappings of Riemannian manifolds”, Amer. J. Math., 86 (1964), 109–160 | DOI | MR | Zbl

[3] Lawson H. B., Simons J., “On stable currents and their applications to global problems in real and complex geometry”, Ann. Math., 98:2 (1973), 427–450 | DOI | MR | Zbl

[4] Fomenko A. T., “Mnogomernye variatsionnye metody v topologii ekstremalei”, UMN, 36:6 (1981), 105–135 | MR | Zbl

[5] Dubrovin B. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya, Nauka, M., 1979 | MR

[6] Novikov S. P., “Gamiltonov formalizm i mnogoznachnyi analog teorii Morsa”, UMN, 37:5 (1982), 3–49 | MR | Zbl

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

[8] Simons J., “Minimal varieties in Riemannian manifolds”, Ann. Math., 88:1 (1968), 66–106 | DOI | MR

[9] Fomenko A. T., “Mnogomernye zadachi Plato na rimanovykh mnogoobraziyakh i ekstraordinarnye teorii gomologii i kogomologii. II”, Trudy semin. po vekt. i tenz. analizu, Vyp. 18, MGU, M., 1978, 4–93 | MR

[10] Smith R. T., “Harmonic mappings of spheres”, Amer. J. Math., 97:2 (1975), 364–387 | DOI | MR

[11] Smith R. T., “The second variation formula for harmonic mappings”, Proc. Amer. Math. Soc., 47:1 (1975), 229–236 | DOI | MR | Zbl

[12] Kobayasi K., Nomidzu K., Osnovy differentsialnoi geometrii, T. 2, Nauka, M., 1981

[13] Goto M., Grosskhans F., Poluprostye algebry Li, Mir, M., 1981 | MR | Zbl

[14] Burbaki N., Gruppy i algebry Li, Mir, M., 1972 | MR | Zbl

[15] Burbaki N., Gruppy i algebry Li, Mir, M., 1978 | MR