Geodesic
Infinitesimal bendings of a class of multidimensional surfaces with boundary
Sbornik. Mathematics, Tome 49 (1984) no. 1, pp. 49-60 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Infinitesimal bendings are considered for a $2k$-dimensional ($k\geqslant1$) surface of class $C^2$ with boundary in $3k$-dimensional Euclidean space in the case when the surface is star-shaped with respect to some $(k-1)$-dimensional plane or projects in a one-to-one manner on some $2k$-dimensional plane. Tests are established for the rigidity of such surfaces under boundary conditions of sliding. Bibliography: 12 titles. 
@article{SM_1984_49_1_a3,
     author = {P. E. Markov},
     title = {Infinitesimal bendings of a~class of multidimensional surfaces with boundary},
     journal = {Sbornik. Mathematics},
     pages = {49--60},
     year = {1984},
     volume = {49},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1984_49_1_a3/}
}
TY  - JOUR
AU  - P. E. Markov
TI  - Infinitesimal bendings of a class of multidimensional surfaces with boundary
JO  - Sbornik. Mathematics
PY  - 1984
SP  - 49
EP  - 60
VL  - 49
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1984_49_1_a3/
LA  - en
ID  - SM_1984_49_1_a3
ER  - 
%0 Journal Article
%A P. E. Markov
%T Infinitesimal bendings of a class of multidimensional surfaces with boundary
%J Sbornik. Mathematics
%D 1984
%P 49-60
%V 49
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1984_49_1_a3/
%G en
%F SM_1984_49_1_a3
P. E. Markov. Infinitesimal bendings of a class of multidimensional surfaces with boundary. Sbornik. Mathematics, Tome 49 (1984) no. 1, pp. 49-60. http://geodesic.mathdoc.fr/item/SM_1984_49_1_a3/

[1] Senkin E. P., “Neizgibaemost vypuklykh poverkhnostei. Dopolnenie”, Ukr. geom. sb., 1974, no. 17, 132–134 | MR

[2] Gorzii T. A., “Zhestkost vypuklykh giperpoverkhnostei ellipticheskogo prostranstva”, Ukr. geom. sb., 1975, no. 18, 66–68 | MR

[3] Markov P. E., “Beskonechno malye izgibaniya nekotorykh mnogomernykh poverkhnostei”, Matem. zametki, 27:3 (1980), 469–479 | MR | Zbl

[4] Jacobowitz H., “Implicit function theorems and isometric embeddings”, Annals of Math., 95:2 (1972), 191–225 | DOI | MR | Zbl

[5] Mur Dzh., “Izometricheskie pogruzheniya rimanovykh proizvedenii”, Issledovaniya po metricheskoi teorii poverkhnostei, Mir, M., 1980, 264–291 | MR

[6] Markov P. E., Beskonechno malye izgibaniya $n$-mernykh poverkhnostei v $m$-mernykh prostranstvakh postoyannoi krivizny, Dis. na soiskanie uch. st. kand. fiz.-matem. nauk, Minsk, 1978

[7] Pogorelov A. V., Vneshnyaya geometriya vypuklykh poverkhnostei, Nauka, M., 1969 | MR

[8] Vekua I. N., Obobschennye analiticheskie funktsii, Fizmatgiz, M., 1969 | MR

[9] Boyarskii B. V., Efimov N. V., “Printsip maksimuma v teorii beskonechno malykh izgibanii poverkhnostei”, UMN, 14:6 (1959), 147–153 | MR

[10] Bitsadze A. V., Kraevye zadachi dlya ellipticheskikh uravnenii vtorogo poryadka, Nauka, M., 1966

[11] Efimov N. V., “Kachestvennye voprosy teorii deformatsii poverkhnostei”, UMN, 3:24 (1948), 47–158 | MR | Zbl

[12] Kon-Fossen S. E., Nekotorye voprosy differentsialnoi geometrii v tselom, Fizmatgiz, M., 1959 | MR