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Combinatorica, ISSN 0209-9683, 08/2016, Volume 36, Issue 4, pp. 417 - 429
Journal Article
Demonstratio Mathematica, ISSN 2391-4661, 03/2010, Volume 43, Issue 1, pp. 187 - 202
In 1998 A. Soranzo introduced the notions of +∞- and −∞-chord functions (see [ ]). In this paper we give an answer to the question when a convex body is... 
52A20
Journal Article
Mathematika, ISSN 0025-5793, 2016, Volume 62, Issue 2, pp. 378 - 405
We investigate the problem of the decomposition of balls into a finite number of congruent pieces in dimension d=2k. In addition, we prove that the... 
52A20 | 52A15 | 51F20 (primary)
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 08/2018, Volume 50, Issue 4, pp. 745 - 752
Let f be an integrable log‐concave function on Rn with the center of mass at the origin. We show that ∫0∞f(sθ)ds⩾e−n∫−∞∞f(sθ)ds for every θ∈Sn−1, and the... 
26B15 | 52A20 (primary) | 26B25 | 26D15 | MATHEMATICS
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 2017, Volume 114, Issue 1, pp. 133 - 158
Let C be a subset of Rn (not necessarily convex), f:C→R be a function and G:C→Rn be a uniformly continuous function, with modulus of continuity ω. We provide a... 
53A99 | 52A20 | 54C20 | 35J96 | 52A41 | 53C45 | 58C25 | 26B05
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 2013, Volume 162, Issue 11, pp. 1895 - 1922
The continuity of the inverse Klain map is investigated and the class of centrally symmetric convex bodies at which every valuation depends continuously on its... 
MATHEMATICS | CENTRALLY SYMMETRIC FACES | VALUED VALUATIONS | CONVEX-BODIES | PROJECTION BODIES | MINKOWSKI-VALUATIONS | INTEGRAL GEOMETRY | MCMULLEN,P. CONJECTURE | COMPLEX VECTOR-SPACES | INTERSECTION BODIES | TRANSLATION-INVARIANT VALUATIONS | Mathematics - Metric Geometry | 52A20 | 52B45 | 52A40
Journal Article
Mathematika, ISSN 0025-5793, 04/2020, Volume 66, Issue 2, pp. 343 - 355
Magnitude is an isometric invariant of metric spaces inspired by category theory. Recent work has shown that the asymptotic behavior under rescaling of the... 
52A20 (primary)
Journal Article
Discrete & computational geometry, ISSN 1432-0444, 2018, Volume 60, Issue 2, pp. 512 - 529
This paper concerns the facial geometry of the set of $$n \times n$$ n×n correlation matrices. The main result states that almost every set of r vertices... 
Cut polytope | Computational Mathematics and Numerical Analysis | Elliptope | Matrix concentration | Correlation matrix | Probabilistic method | 15B48 | Mathematics | 90C27 | Secondary: 52B12 | Combinatorics | Face | Primary: 52A20 | MATHEMATICS | OPTIMIZATION | COMPUTER SCIENCE, THEORY & METHODS | MAX-CUT PROBLEM | Correlation
Journal Article
Mathematika, ISSN 0025-5793, 2018, Volume 64, Issue 1, pp. 1 - 19
Employing the inverse function theorem on Banach spaces, we prove that in a $C^{2}(S^{n-1})$ -neighborhood of the unit ball, the only solutions of... 
52A20 | 53A15 (primary) | MATHEMATICS | MATHEMATICS, APPLIED | BODIES | Mathematics - Metric Geometry
Journal Article
Mathematika, ISSN 0025-5793, 2017, Volume 63, Issue 2, pp. 372 - 382
Let $n\geqslant C$ for a large universal constant $C>0$ and let $B$ be a convex body in $\mathbb{R}^{n}$ such that for any $(x_{1},x_{2},\ldots ,x_{n})\in B$ ,... 
52A20 | 52C17 (primary) | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Forum Mathematicum, ISSN 0933-7741, 03/2019, Volume 31, Issue 2, pp. 479 - 489
In [G. Bianchi, R. J. Gardner and P. Gronchi, Symmetrization in geometry, Adv. Math. 306 2017, 51–88], a systematic study of symmetrization operators on convex... 
52A20 | intrinsic volumes | 52A39 | Symmetrization | 52A38 | MATHEMATICS | MATHEMATICS, APPLIED | Operators | Convexity | Questions
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2016, Volume 2016, Issue 23, pp. 7230 - 7252
In this article, we consider the following analog of Bezout inequality for mixed volumes: V(P-1,..., P-r, Delta(n-r))V-n(Delta)(r-1) <= Pi(r)(i=1) V(P-i,... 
MATHEMATICS
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 6/2014, Volume 51, Issue 4, pp. 926 - 963
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 08/2016, Volume 271, Issue 3, pp. 610 - 619
We provide a sharp lower bound for the perimeter of the inner parallel sets of a convex body Ω. The bound depends only on the perimeter and inradius r of the... 
Convex geometry | Perimeter | Inner parallel sets | MATHEMATICS
Journal Article
Aequationes mathematicae, ISSN 1420-8903, 2018, Volume 92, Issue 5, pp. 949 - 961
Euclidean geometry is the only Minkowski geometry in which either there is a centrally symmetric, or a quadratic conic, or there is a conical ellipsoid or... 
52A20 | Conics | Analysis | 53A35 | Projective metric | 51M09 | Minkowski geometry | Mathematics | Combinatorics | MATHEMATICS | MATHEMATICS, APPLIED | Geometry | Euclidean geometry
Journal Article
Journal of Geometry, ISSN 0047-2468, 4/2019, Volume 110, Issue 1, pp. 1 - 20
We extend to arbitrary finite n the notion of immobilization of a convex body O in $${\mathbb {R}}^n$$ Rn by a finite set of points $${\mathcal {P}}$$ P in the... 
Geometry | contact points | Secondary 52A15 | n -simplex | Primary 52A20 | Immobilization | Mathematics
Journal Article
Mathematika, ISSN 0025-5793, 2019, Volume 65, Issue 3, pp. 500 - 504
Using previous results about shadow systems and Steiner symmetrization, we prove that the local maximizers of the volume product of convex bodies are actually... 
52A20 | 52A40 (primary) | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES
Journal Article
Journal of the London Mathematical Society, ISSN 1469-7750, 2019, Volume 100, Issue 2, pp. 425 - 446
We study a new construction of bodies from a given convex body in Rn which are isomorphic to (weighted) floating bodies. We establish several properties of... 
52A20 | 52A38 (primary) | 52A27
Journal Article
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