28 citations · 44 across the 8 of their papers we have counts for
16 papers
On convex bodies with rotationally symmetric planar projections
Sergii Myroshnychenko, Dmitry Ryabogin, Christos Saroglou
Let and let be a convex body. For a two-dimensional linear subspace , let be the orthogonal projection of onto . We…
Uniqueness when the curvature is close to be a constant for
Károly J. Böröczky, Christos Saroglou
For fixed positive integer , , , we prove that if a function is sufficiently close to 1, in the sense, then there…
On a -Santaló Conjecture
Pavlos Kalantzopoulos, Christos Saroglou
Let be an integer. In the spirit of Kolesnikov-Werner \cite{KW}, for each , we conjecture a sharp Santaló type inequality (we call it -Santaló conj…
A non-existence result for the -Minkowski problem
Christos Saroglou
We show that given a real number , a positive integer and a proper subspace of , the measure on the Euclidean sphere , which is concent…
On a non-homogeneous version of a problem of Firey
Christos Saroglou
We investigate the uniqueness for the Monge-Ampère type equation \begin{equation} \label{eq-abstract} det(u_{ij}+δ_{ij}u)_{i,j=1}^{n-1}=G(u),\ \ \ \ \ \ \ (*)\end{equation}on $S^{n…
Functions with isotropic sections
Ioannis Purnaras, Christos Saroglou
We prove a local version of a recently established theorem by Myroshnychenko, Ryabogin and the second named author. More specifically, we show that if , $g:\mathbb{S}^{n-1…
On some problems concerning symmetrization operators
Christos Saroglou
In [G. Bianchi, R. J. Gardner and P. Gronchi, Symmetrization in Geometry, Adv. Math., vol. 306 (2017), 51-88], a systematic study of symmetrization operators on convex sets and the…
Wulff shapes and a characterization of simplices via a Bezout type inequality
Christos Saroglou, Ivan Soprunov, Artem Zvavitch
Inspired by a fundamental theorem of Bernstein, Kushnirenko, and Khovanskii we study the following Bezout type inequality for mixed volumes $$ V(L_1,\dots,L_{n})V_n(K)\leq V(L_1,K[…
Star bodies with completely symmetric sections
Sergii Myroshnychenko, Dmitry Ryabogin, Christos Saroglou
We say that a star body is completely symmetric if it has centroid at the origin and its symmetry group forces any ellipsoid whose symmetry group contains , to be a ball…
Estimating volume and surface area of a convex body via its projections or sections
Alexander Koldobsky, Christos Saroglou, Artem Zvavitch
The main goal of this paper is to present a series of inequalities connecting the surface area measure of a convex body and surface area measure of its projections and sections. We…
Characterization of Simplices via the Bezout Inequality for Mixed volumes
Christos Saroglou, Ivan Soprunov, Artem Zvavitch
We consider the following Bezout inequality for mixed volumes: It was shown…
Iterations of the projection body operator and a remark on Petty's conjectured projection inequality
Christos Saroglou, Artem Zvavitch
We prove that if a convex body has absolutely continuous surface area measure, whose density is sufficiently close to the constant, then the sequence of convex bodies co…
On the shape of a convex body with respect to its second projection body
Christos Saroglou
We prove results relative to the problem of finding sharp bounds for the affine invariant . Namely, we prove that if is a 3-dimensional zonoid of volume…
More on logarithmic sums of convex bodies
Christos Saroglou
We prove that the log-Brunn-Minkowski inequality (log-BMI) for the Lebesque measure in dimension would imply the log-BMI and, therefore, the B-conjecture for any log-concave de…
On the equivalence between two problems of asymmetry on convex bodies
Christos Saroglou
The simplex was conjectured to be the extremal convex body for the two following "problems of asymmetry":\\ P1) What is the minimal possible value of the quantity $\max_{K'} |K'|/|…
Remarks on the conjectured log-Brunn-Minkowski inequality
Christos Saroglou
\footnotesize Böröczky, Lutwak, Yang and Zhang recently conjectured a certain strengthening of the Brunn-Minkowski inequality for symmetric convex bodies, the so-called log-Brunn-M…