Geodesic
On some vector balancing problems
Studia Mathematica, Tome 122 (1997) no. 3, pp. 225-234

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

DOI

Let V be an origin-symmetric convex body in $ℝ^n$, n≥ 2, of Gaussian measure $γ_n(V)≥ 1/2$. It is proved that for every choice $u_1,...,u_n$ of vectors in the Euclidean unit ball $B_n$, there exist signs $ε_j ∈ {-1,1}$ with $ε_{1}u_{1} + ... + ε_{n}u_{n} ∈ (clogn)V$. The method used can be modified to give simple proofs of several related results of J. Spencer and E. D. Gluskin. 
Apostolos A.  Giannopoulos. On some vector balancing problems. Studia Mathematica, Tome 122 (1997) no. 3, pp. 225-234. doi: 10.4064/sm-122-3-225-234
@article{10_4064_sm_122_3_225_234,
     author = {Apostolos A.  Giannopoulos},
     title = {On some vector balancing problems},
     journal = {Studia Mathematica},
     pages = {225--234},
     year = {1997},
     volume = {122},
     number = {3},
     doi = {10.4064/sm-122-3-225-234},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-122-3-225-234/}
}
TY  - JOUR
AU  - Apostolos A.  Giannopoulos
TI  - On some vector balancing problems
JO  - Studia Mathematica
PY  - 1997
SP  - 225
EP  - 234
VL  - 122
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-122-3-225-234/
DO  - 10.4064/sm-122-3-225-234
LA  - en
ID  - 10_4064_sm_122_3_225_234
ER  - 
%0 Journal Article
%A Apostolos A.  Giannopoulos
%T On some vector balancing problems
%J Studia Mathematica
%D 1997
%P 225-234
%V 122
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-122-3-225-234/
%R 10.4064/sm-122-3-225-234
%G en
%F 10_4064_sm_122_3_225_234

Cité par Sources :