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

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)

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

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

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

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)

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

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

Mathematical Programming, ISSN 0025-5610, 10/2015, Volume 153, Issue 1, pp. 223 - 245

Hyperbolic polynomials are real polynomials whose real hypersurfaces are maximally nested ovaloids, the innermost of which is convex. These polynomials appear...

52A20 | 11E25 | Mathematical Methods in Physics | Primary 14P99 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C22 | Mathematics | Combinatorics | Secondary 05E99 | HALF-PLANE PROPERTY | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INEQUALITY | Studies | Geometry | Theorems | Mathematical models | Polynomials | Optimization | Mathematical programming | Approximation | Mathematical analysis | Differential equations | Spectra | Combinatorial analysis | Sums

52A20 | 11E25 | Mathematical Methods in Physics | Primary 14P99 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C22 | Mathematics | Combinatorics | Secondary 05E99 | HALF-PLANE PROPERTY | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INEQUALITY | Studies | Geometry | Theorems | Mathematical models | Polynomials | Optimization | Mathematical programming | Approximation | Mathematical analysis | Differential equations | Spectra | Combinatorial analysis | Sums

Journal Article

10.
Full Text
A LOCAL UNIQUENESS THEOREM FOR MINIMIZERS OF PETTY’S CONJECTURED PROJECTION INEQUALITY

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

52A20 | 53A15 (primary) | MATHEMATICS | MATHEMATICS, APPLIED | BODIES | Mathematics - Metric Geometry

Journal Article

Foundations of Computational Mathematics, ISSN 1615-3375, 12/2019, Volume 19, Issue 6, pp. 1223 - 1263

Consider a finite system of non-strict polynomial inequalities with solution set $$S\subseteq \mathbb R^n$$ S ⊆ R n . Its Lasserre relaxation of degree d is a...

52A20 | Positive polynomial | 52A41 | Semidefinitely representable set | Secondary: 12D15 | Mathematics | Moment relaxation | 46L30 | Primary: 13J30 | Linear matrix inequality | Applications of Mathematics | Math Applications in Computer Science | Economics, general | Lasserre relaxation | Spectrahedron | Semidefinite programming | Sum of squares | 14P10 | Linear and Multilinear Algebras, Matrix Theory | 90C26 | Basic closed semialgebraic set | Pure state | Polynomial optimization | Numerical Analysis | 90C22 | Computer Science, general | Approximation theory | Fields, Algebraic | Research | Mathematical research | Mathematical analysis | Polynomials | Hulls (structures) | Linear matrix inequalities | Convexity | Matrix methods | Optimization

52A20 | Positive polynomial | 52A41 | Semidefinitely representable set | Secondary: 12D15 | Mathematics | Moment relaxation | 46L30 | Primary: 13J30 | Linear matrix inequality | Applications of Mathematics | Math Applications in Computer Science | Economics, general | Lasserre relaxation | Spectrahedron | Semidefinite programming | Sum of squares | 14P10 | Linear and Multilinear Algebras, Matrix Theory | 90C26 | Basic closed semialgebraic set | Pure state | Polynomial optimization | Numerical Analysis | 90C22 | Computer Science, general | Approximation theory | Fields, Algebraic | Research | Mathematical research | Mathematical analysis | Polynomials | Hulls (structures) | Linear matrix inequalities | Convexity | Matrix methods | Optimization

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

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

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

MATHEMATICS

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 6/2014, Volume 51, Issue 4, pp. 926 - 963

The intrinsic volumes of a convex cone are geometric functionals that return basic structural information about the cone. Recent research has demonstrated that...

60D05 | Steiner formula | Computational Mathematics and Numerical Analysis | Primary 52A22 | Geometric probability | Secondary 52A20 | Mathematics | Concentration inequality | Intrinsic volume | Combinatorics | Convex cone | Statistical dimension | MATHEMATICS | NUMBER | SPHERES | COMPUTER SCIENCE, THEORY & METHODS | Geometry | Probability | Applied mathematics | Conics | Cones | Mathematical analysis | Inequalities | Projection | Gaussian | Vectors (mathematics) | Optimization | Mathematics - Metric Geometry

60D05 | Steiner formula | Computational Mathematics and Numerical Analysis | Primary 52A22 | Geometric probability | Secondary 52A20 | Mathematics | Concentration inequality | Intrinsic volume | Combinatorics | Convex cone | Statistical dimension | MATHEMATICS | NUMBER | SPHERES | COMPUTER SCIENCE, THEORY & METHODS | Geometry | Probability | Applied mathematics | Conics | Cones | Mathematical analysis | Inequalities | Projection | Gaussian | Vectors (mathematics) | Optimization | Mathematics - Metric Geometry

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

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

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

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

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

52A20 | 52A38 (primary) | 52A27

Journal Article

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