Geodesic
Extremal values of the integral of the mean curvature on the set of parallelepipeds with a given geodesic diameter
Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 2, pp. 77-81 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the paper, extremal values of the mean curvature integral on set of parallelepipeds with a given geodesic diameter are obtained. The maximal (minimal) value of the integral of mean curvature is attained for a degenerate parallelepiped with relation $0:1:1$ ($0:0:1$, respectively) for its edge lengths. 
@article{VMJ_2013_15_2_a8,
     author = {N. V. Rasskazova},
     title = {Extremal values of the integral of the mean curvature on the set of parallelepipeds with a~given geodesic diameter},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {77--81},
     year = {2013},
     volume = {15},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2013_15_2_a8/}
}
TY  - JOUR
AU  - N. V. Rasskazova
TI  - Extremal values of the integral of the mean curvature on the set of parallelepipeds with a given geodesic diameter
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2013
SP  - 77
EP  - 81
VL  - 15
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMJ_2013_15_2_a8/
LA  - ru
ID  - VMJ_2013_15_2_a8
ER  - 
%0 Journal Article
%A N. V. Rasskazova
%T Extremal values of the integral of the mean curvature on the set of parallelepipeds with a given geodesic diameter
%J Vladikavkazskij matematičeskij žurnal
%D 2013
%P 77-81
%V 15
%N 2
%U http://geodesic.mathdoc.fr/item/VMJ_2013_15_2_a8/
%G ru
%F VMJ_2013_15_2_a8
N. V. Rasskazova. Extremal values of the integral of the mean curvature on the set of parallelepipeds with a given geodesic diameter. Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 2, pp. 77-81. http://geodesic.mathdoc.fr/item/VMJ_2013_15_2_a8/

[1] Vyalyi M. N., “Kratchaishie puti po poverkhnosti parallelepipeda”, Mat. prosveschenie. Ser. 3, 9, MTsNMO, M., 2005, 203–206

[2] Nikonorov Yu. G., Nikonorova Yu. V., “O vnutrennem rasstoyanii na poverkhnosti parallelepipeda”, Tr. Rubtsovskogo industr. in-ta, 9, 2000, 222–228

[3] Santalo L. A., Integralnaya geometriya i geometricheskie veroyatnosti, Nauka, M., 1983, 360 pp. | MR | Zbl

[4] Khadviger G., Lektsii ob ob'eme, ploschadi poverkhnosti i izoperimetrii, Nauka, M., 1966, 416 pp.

[5] Nikonorov Yu. G., Nikonorova Yu. V., “The intrinsic diameter of the surface of a parallelepiped”, Discrete and Computational Geometry, 40 (2008), 504–527 | DOI | MR | Zbl