Geodesic
Research of stability for extremal rotation surfaces
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 7 (2007) no. 2, pp. 25-32 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this work we obtain the first and second variations of area type functional for rotation surfaces formulas. We proof the feature of stability and instability in the terms of the local coordinates and special integrals. We consider some examples by application our results for research if stability for rotation surfaces. 
@article{ISU_2007_7_2_a5,
     author = {N. M. Medvedeva},
     title = {Research of stability for extremal rotation surfaces},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {25--32},
     year = {2007},
     volume = {7},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2007_7_2_a5/}
}
TY  - JOUR
AU  - N. M. Medvedeva
TI  - Research of stability for extremal rotation surfaces
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2007
SP  - 25
EP  - 32
VL  - 7
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ISU_2007_7_2_a5/
LA  - ru
ID  - ISU_2007_7_2_a5
ER  - 
%0 Journal Article
%A N. M. Medvedeva
%T Research of stability for extremal rotation surfaces
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2007
%P 25-32
%V 7
%N 2
%U http://geodesic.mathdoc.fr/item/ISU_2007_7_2_a5/
%G ru
%F ISU_2007_7_2_a5
N. M. Medvedeva. Research of stability for extremal rotation surfaces. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 7 (2007) no. 2, pp. 25-32. http://geodesic.mathdoc.fr/item/ISU_2007_7_2_a5/

[1] Dubrovin B. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya: Metody i prilozheniya, Nauka, gl. red. fiz.-mat. lit., M., 1986, 760 pp. | MR

[2] Klyachin V. A., Miklyukov V. M., “Maksimalnye giperpoverkhnosti trubchatogo tipa v prostranstve Minkovskogo”, Izv. AN SSSR. Ser. mat., 55:1 (1991), 206–217 | MR

[3] Tuzhilin A. A., “Indeksy tipa Morsa dvumernykh minimalnykh poverkhnostei v $\mathbb R^3$ i $\mathbb H^3$”, Izv. AN SSSR. Ser. mat., 55:2 (1991), 581–607 | MR

[4] Tuzhilin A. A., Fomenko A. T., Elementy geometrii i topologii minimalnykh poverkhnostei, Nauka, M., 1991, 174 pp. | MR

[5] Klyachin V. A., Medvedeva N. M., Ob ustoichivosti ekstremalnykh poverkhnostei nekotorykh funktsionalov tipa ploschadi, Dep. v VINITI 08.11.06 No 1313-B, Volgograd, 2006, 23 pp.; Сибирские электронные математические известия. Статьи, 4 (2007), 113–132 | MR | Zbl

[6] Tkachev V. G., “External Geometry of $p$-Minimal Surfaces”, Geometry from the Pacific Rim, eds. Berrick/Loo/Wang, Walter de Gruyter, Berlin, 1997, 363–375 | MR | Zbl

[7] Poznyak E. G., Shikin E. V., Differentsialnaya geometriya: pervoe znakomstvo, Izd-vo MGU, M., 1990, 384 pp. | Zbl

[8] Klyachin V. A., Miklyukov V. M., “Priznaki neustoichivosti poverkhnostei nulevoi srednei krivizny v iskrivlennykh lorentsevykh proizvedeniyakh”, Mat. sb., 187:11 (1996), 67–88 | DOI | MR | Zbl

[9] Khardi G. G., Littlvud Dzh. E., Polia G., Neravenstva, Gos. izd-vo inostr. lit., M., 1948, 250 pp.