#### Filter Results:

#### Publication Year

1999

2017

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

#### Method

Learn More

We provide a generalization of John's representation of the identity for the maximal volume position of L inside K, where K and L are arbitrary smooth convex bodies in R n. >From this representation we obtain Banach-Mazur distance and volume ratio estimates.

- N. Dafnis, A. Giannopoulos, A. Tsolomitis
- 2012

Let K be an isotropic convex body in R xN are independent random points, uniformly distributed in K. We prove that if n 2 N exp(√ n) then the normalized quermaßintegrals

Let K be a convex body in R n and let W i (K), i = 1,. .. , n − 1 be its quermassintegrals. We study minimization problems of the form min{W i (T K) | T ∈ SL n } and show that bodies which appear as solutions of such problems satisfy isotropic conditions or even admit an isotropic characterization for appropriate measures. This shows that several well known… (More)

- N. Dafnis, A. Giannopoulos, O. Guédon
- 2008

Let K be an isotropic 1-unconditional convex body in R n. For every N > n consider N independent random points x1,. .. , xN uniformly distributed in K. We prove that, with probability greater than 1 − C 1 exp(−cn) if N ≥ c 1 n and greater than 1−C 1 exp(−cn/ log n) if n < N < c 1 n, the random

- Iraklis Giannakis, Antonios Giannopoulos, Alexander Yarovoy
- IEEE Trans. Geoscience and Remote Sensing
- 2016

- Craig Warren, Antonios Giannopoulos
- Signal Processing
- 2017

- Craig Warren, Antonios Giannopoulos, Iraklis Giannakis
- Computer Physics Communications
- 2016

- A. Giannopoulos, G. Paouris, P. Valettas
- 2011

It is known that every isotropic convex body K in R n has a " subgaussian " direction with constant r = O(√ log n). This follows from the upper bound |Ψ2(K)| 1/n c √ log n √ n LK for the volume of the body Ψ2(K) with support function h Ψ 2 (K) (θ) := sup 2qn ·,θq √ q. The approach in all the related works does not provide estimates on the measure of… (More)

The purpose of this article is to describe a reduction of the slicing problem to the study of the parameter I1(K, Z • q (K)) = K