Geodesic
Exceptional directions for a convex body
Matematičeskie zametki, Tome 20 (1976) no. 3, pp. 365-371 
B. A. Ivanov. Exceptional directions for a convex body. Matematičeskie zametki, Tome 20 (1976) no. 3, pp. 365-371. http://geodesic.mathdoc.fr/item/MZM_1976_20_3_a7/
@article{MZM_1976_20_3_a7,
     author = {B. A. Ivanov},
     title = {Exceptional directions for a~convex body},
     journal = {Matemati\v{c}eskie zametki},
     pages = {365--371},
     year = {1976},
     volume = {20},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_3_a7/}
}
TY  - JOUR
AU  - B. A. Ivanov
TI  - Exceptional directions for a convex body
JO  - Matematičeskie zametki
PY  - 1976
SP  - 365
EP  - 371
VL  - 20
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_1976_20_3_a7/
LA  - ru
ID  - MZM_1976_20_3_a7
ER  - 
%0 Journal Article
%A B. A. Ivanov
%T Exceptional directions for a convex body
%J Matematičeskie zametki
%D 1976
%P 365-371
%V 20
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1976_20_3_a7/
%G ru
%F MZM_1976_20_3_a7

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

Let $K$ be a convex body in Rn andO be a point inside $K$. We examine the Grassmann manifold of $k$-planes passing through $O$. We take as exceptional the planes intersecting $K$ along a body having at least one $(k-1)$-dimensional face such that it does not have points inside the hyperfaces of body $K$. We prove that in the Grassmann manifold $G_k^n$ the set of such exceptional planes is of measure zero.