The best ways to slice a Polytope
We study the structure of the set of all possible affine hyperplane sections of a convex
polytope. We present two different cell decompositions of this set, induced by hyperplane …
polytope. We present two different cell decompositions of this set, induced by hyperplane …
Inequalities for sections and projections of convex bodies
A Giannopoulos, A Koldobsky… - Harmonic analysis and …, 2023 - degruyter.com
This chapter belongs to the area of geometric tomography, which is the study of geometric
properties of solids based on data about their sections and projections. We describe a new …
properties of solids based on data about their sections and projections. We describe a new …
Polynomial bounds in Koldobsky's discrete slicing problem
In 2013, Koldobsky posed the problem to find a constant $ d_n $, depending only on the
dimension $ n $, such that for any origin-symmetric convex body $ K\subset\mathbb {R}^ n …
dimension $ n $, such that for any origin-symmetric convex body $ K\subset\mathbb {R}^ n …
On Rogers–Shephard-type inequalities for the lattice point enumerator
D Alonso-Gutiérrez, E Lucas… - Communications in …, 2023 - World Scientific
In this paper, we study various Rogers–Shephard-type inequalities for the lattice point
enumerator G n (⋅) on ℝ n. In particular, for any non-empty convex bounded sets K, L⊂ ℝ n …
enumerator G n (⋅) on ℝ n. In particular, for any non-empty convex bounded sets K, L⊂ ℝ n …
A Remark on discrete Brunn–Minkowski type inequalities via transportation of measure
BA Slomka - Israel Journal of Mathematics, 2024 - Springer
We give an alternative proof for discrete Brunn–Minkowski type inequalities, recently
obtained by Halikias, Klartag and the author. This proof also implies somewhat stronger …
obtained by Halikias, Klartag and the author. This proof also implies somewhat stronger …
On Discrete LOG-Brunn--Minkowski Type Inequalities
MA Hernández Cifre, E Lucas - SIAM Journal on Discrete Mathematics, 2022 - SIAM
The conjectured log-Brunn--Minkowski inequality says that the volume of centrally symmetric
convex bodies K,L⊂R^n satisfies vol\bigl((1-λ)⋅K+_0λ⋅L\bigr)≧vol(K)^1-λvol(L)^λ …
convex bodies K,L⊂R^n satisfies vol\bigl((1-λ)⋅K+_0λ⋅L\bigr)≧vol(K)^1-λvol(L)^λ …