Geodesic
Two Applications of Topology to Convex Geometry
Informatics and Automation, Geometric topology and set theory, Tome 247 (2004), pp. 182-185.

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

The purpose of this paper is to prove two theorems of convex geometry using the techniques of topology. The first theorem states that if, for a strictly convex body $K$, one may choose continuously a centrally symmetric section, then $K$ must be centrally symmetric. The second theorem states that if every section of a three-dimensional convex body $K$ through the origin has an axis of symmetry, then there is a section of $K$ through the origin which is a disk. 
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L. Montejano. Two Applications of Topology to Convex Geometry. Informatics and Automation, Geometric topology and set theory, Tome 247 (2004), pp. 182-185. http://geodesic.mathdoc.fr/item/TRSPY_2004_247_a11/

[1] Aitchison P. W., Petty C. M., Rogers C. A., “A convex body with a false centre is an ellipsoid”, Mathematika, 18 (1971), 50–59 | DOI | MR | Zbl

[2] Larman D. G., “A note in the false centre problem”, Mathematika, 21 (1974), 216–227 | DOI | MR

[3] Mani P., “Fields of planar bodies tangent to spheres”, Monatsh. Math., 74 (1970), 145–149 | DOI | MR | Zbl

[4] Montejano L., “Convex bodies with homothetic sections”, Bull. London Math. Soc., 23 (1991), 381–386 | DOI | MR | Zbl

[5] Rogers C. A., “Sections and projections of convex bodies”, Port. Math., 24 (1965), 99–103 | MR | Zbl