9 citations · 21 across the 11 of their papers we have counts for
8 papers · 1 filter
Illuminating 1-unconditional convex bodies in and , and certain cases in higher dimensions
Wen Rui Sun, Beatrice-Helen Vritsiou
We settle the Hadwiger-Boltyanski Illumination Conjecture for all 1-unconditional convex bodies in and in . Moreover, we settle the conjecture for th…
On the illumination of 1-symmetric convex bodies
Wen Rui Sun, Beatrice-Helen Vritsiou
In ["Illumination of convex bodies with many symmetries", Mathematika 63 (2017)], Tikhomirov verified the Hadwiger-Boltyanski Illumination Conjecture for the class of 1-symmetric c…
Regular ellipsoids and a Blaschke-Santaló-type inequality for projections of non-symmetric convex bodies
Beatrice-Helen Vritsiou
It is shown that every not-necessarily symmetric convex body in has an affine image of such that the covering numbers of by growing…
A note on volume thresholds for random polytopes
Debsoumya Chakraborti, Tomasz Tkocz, Beatrice-Helen Vritsiou
We study the expected volume of random polytopes generated by taking the convex hull of independent identically distributed points from a given distribution. We show that for log-c…
Asymptotic normality for random simplices and convex bodies in high dimensions
David Alonso-Gutiérrez, Florian Besau, Julian Grote +5
Central limit theorems for the log-volume of a class of random convex bodies in are obtained in the high-dimensional regime, that is, as . In particular,…
Improved bounds for Hadwiger's covering problem via thin-shell estimates
Han Huang, Boaz A. Slomka, Tomasz Tkocz +1
A central problem in discrete geometry, known as Hadwiger's covering problem, asks what the smallest natural number is such that every convex body in ${\mathbb R}…
Further unifying two approaches to the hyperplane conjecture
Beatrice-Helen Vritsiou
We compare and combine two approaches that have been recently introduced by Dafnis and Paouris [DP] and by Klartag and Milman [KM] with the aim of providing bounds for the isotropi…
The isotropic position and the reverse Santaló inequality
Apostolos Giannopoulos, Grigoris Paouris, Beatrice-Helen Vritsiou
We present proofs of the reverse Santaló inequality, the existence of M-ellipsoids and the reverse Brunn-Minkowski inequality, using purely convex geometric tools. Our approach is…