On some vector balancing problems

Tom 122 / 1997

Apostolos A. Giannopoulos Studia Mathematica 122 (1997), 225-234 DOI: 10.4064/sm-122-3-225-234

Streszczenie

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.

Autorzy

  • Apostolos A. Giannopoulos

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