Geodesic
Reconstruction of centrally symmetric convex bodies in $\mathbb{R}^n$
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2011), pp. 28-32 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The article considers the problem of existence and uniqueness of a centrally symmetric convex body in $\mathbb R^n$ for which the projection curvature radius function coincides with given function. A necessary and sufficient condition is found that ensures a positive answer. Also we find a representation for the support function of a centrally symmetric convex body. 
@article{BASM_2011_1_a1,
     author = {R. H. Aramyan},
     title = {Reconstruction of centrally symmetric convex bodies in $\mathbb{R}^n$},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {28--32},
     year = {2011},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2011_1_a1/}
}
TY  - JOUR
AU  - R. H. Aramyan
TI  - Reconstruction of centrally symmetric convex bodies in $\mathbb{R}^n$
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2011
SP  - 28
EP  - 32
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/BASM_2011_1_a1/
LA  - en
ID  - BASM_2011_1_a1
ER  - 
%0 Journal Article
%A R. H. Aramyan
%T Reconstruction of centrally symmetric convex bodies in $\mathbb{R}^n$
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2011
%P 28-32
%N 1
%U http://geodesic.mathdoc.fr/item/BASM_2011_1_a1/
%G en
%F BASM_2011_1_a1
R. H. Aramyan. Reconstruction of centrally symmetric convex bodies in $\mathbb{R}^n$. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2011), pp. 28-32. http://geodesic.mathdoc.fr/item/BASM_2011_1_a1/

[1] Ambartzumian R. V., “Combinatorial integral geometry, metric and zonoids”, Acta Appl. Math., 9 (1987), 3–27 | DOI | MR | Zbl

[2] Journal of Contemporary Math. Anal. (Armenian Academy of Sciences) | MR

[3] Journal of Contemporary Math. Anal. (Armenian Academy of Sciences) | MR

[4] Bakelman I. Ya, Verner A. L., Kantor B. E., Differential Geometry in the Large, Nauka, Moscow, 1973 | MR | Zbl

[5] Blaschke W., Kreis und Kugel, (Veit, Leipzig), 2nd Ed., De Gruyter, Berlin, 1956 | MR | Zbl

[6] Firey W. J., “Intermediate christoffel-minkowski problems for figures of revolution”, Israel Journal of Mathematics, 8:4 (1970), 384–390 | DOI | MR | Zbl

[7] Wiel W., Schneider R., Zonoids and related Topics, Convexity and its Applications, eds. P. Gruber, J. Wills, Birkhauser, Basel, 1983 | MR

[8] Goody P., Wiel W., Zonoids and Generalisations, Handbook of Convex Geometry, eds. P. Gruber, J. Wills, Birkhauser, Basel, 1993