A. Koldobsky

activity

20072026

most citedOn polynomially integrable convex bodies

2 citations · 6 across the 12 of their papers we have counts for

collaborators

Showing math.MGShow all

11 papers · 1 filter

math.MG2021

Inequalities for the Radon transform on convex sets

Apostolos Giannopoulos, Alexander Koldobsky, Artem Zvavitch

Several years ago the authors started looking at some problems of convex geometry from a more general point of view, replacing volume by an arbitrary measure. This approach led to…

math.MG2018

On the maximal perimeter of sections of the cube

Hermann Koenig, Alexander Koldobsky

We prove that the (n-2)-dimensional surface area (perimeter) of central hyperplane sections of the n-dimensional unit cube is maximal for the hyperplane perpendicular to the vector…

math.MG2017

Estimates for moments of general measures on convex bodies

Sergey Bobkov, Bo'az Klartag, Alexander Koldobsky

We prove several estimates for the moments of arbitrary measures on convex bodies. We apply these estimates to show a new slicing inequality for measures on convex bodies. We also…

math.MG2017

An example related to the slicing inequality for general measures

Bo'az Klartag, Alexander Koldobsky

For $n \in N$ let $S_{n}$ be the smallest number $S > 0$ satisfying the inequality $\int_{K} f \leq S \cdot ∣ K ∣^{\frac{1}{n}} \cdot ξ \in S^{n - 1} max \int_{K \cap ξ^{⊥}} f$ for…

math.MG2017★ 2 cited

On polynomially integrable convex bodies

Alexander Koldobsky, Alexander Merkurjev, Vladyslav Yaskin

An infinitely smooth convex body in $R^{n}$ is called polynomially integrable of degree $N$ if its parallel section functions are polynomials of degree $N$ . We prove that the…

math.MG2015

Isomorphic Busemann-Petty problem for sections of proportional dimensions

Alexander Koldobsky

We formulate an isomorphic version of the Busemann-Petty problem and solve it in affirmative in the case of sections of proportional dimensions.