Geodesic
Estimates for the Gaussian curvature of a strictly convex surface and its integral parameters
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 14 (2018) no. 1, pp. 3-15 
V. I. Babenko. Estimates for the Gaussian curvature of a strictly convex surface and its integral parameters. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 14 (2018) no. 1, pp. 3-15. http://geodesic.mathdoc.fr/item/JMAG_2018_14_1_a0/
@article{JMAG_2018_14_1_a0,
     author = {V. I. Babenko},
     title = {Estimates for the {Gaussian} curvature of a strictly convex surface and its integral parameters},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {3--15},
     year = {2018},
     volume = {14},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2018_14_1_a0/}
}
TY  - JOUR
AU  - V. I. Babenko
TI  - Estimates for the Gaussian curvature of a strictly convex surface and its integral parameters
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2018
SP  - 3
EP  - 15
VL  - 14
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JMAG_2018_14_1_a0/
LA  - en
ID  - JMAG_2018_14_1_a0
ER  - 
%0 Journal Article
%A V. I. Babenko
%T Estimates for the Gaussian curvature of a strictly convex surface and its integral parameters
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2018
%P 3-15
%V 14
%N 1
%U http://geodesic.mathdoc.fr/item/JMAG_2018_14_1_a0/
%G en
%F JMAG_2018_14_1_a0

Voir la notice de l'article provenant de la source Math-Net.Ru

Closed and non-closed (with planar edges) strictly convex surfaces with continuous curvatures are considered. Upper and lower bounds are obtained for the Gaussian curvature under various restrictions imposed on integral parameters of a surface: the diameter and width of the surface, the volume of the enclosed body, the maximum area of planar cross-sections of the enclosed body, the radius of a circumscribed or inscribed ball, the height of non-closed surface and the area enclosed by the planar boundary of the surface.

[1] V. I. Babenko, “On the geometrical theory of stability loss of clamped strictly convex shells at external pressure”, Dopov. Nats. Akad. Nauk Ukraïni, 7, 1993, 46–49 (Russian) | Zbl

[2] W. Blaschke, Kreis und Kugel, Walter de Guiter, Berlin, 1956 (German) | MR | Zbl

[3] H. Busemann, Convex Surfaces, Interscience Publishers, Inc., New York, 1958 | MR | Zbl

[4] E. Jahnke, F. Emde, Tables of Functions with Formulae and Curves, Dover Publications, New York, N.Y., 1945 | MR | Zbl

[5] Translations of Mathematical Monographs, 72, Amer. Math. Soc., Providence, RI, 1988 | DOI | MR | Zbl

[6] P. K. Rashevsky, Course of Differential Geometry, GITTL, M., 1956 (Russian)