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Displaying 1 – 18 of 18

Balancing vectors and convex bodies

Wojciech Banaszczyk (1993)

Studia Mathematica

Let U, V be two symmetric convex bodies in $ℝ^{n}$ and |U|, |V| their n-dimensional volumes. It is proved that there exist vectors $u_{1}, . . ., u_{n} \in U$ such that, for each choice of signs $ε_{1}, . . ., ε_{n} = \pm 1$ , one has $ε_{1} u_{1} + . . . + ε_{n} u_{n} \notin r V$ where $r = {(2 π e^{2})}^{- 1 / 2} n^{1 / 2} (| U | / {| V |)}^{1 / n}$ . Hence it is deduced that if a metrizable locally convex space is not nuclear, then it contains a null sequence $(u_{n})$ such that the series $\sum_{n = 1}^{\infty} ε_{n} u_{π (n)}$ is divergent for any choice of signs $ε_{n} = \pm 1$ and any permutation π of indices.

Ball versus distance convexity of metric spaces.

Foertsch, Thomas (2004)

Beiträge zur Algebra und Geometrie

Banach spaces which are semi-L-summands in their biduals.

Rafael Payá, Angel Rodríguez Palacios (1991)

Mathematische Annalen

Banach-Mazur distance of central sections of a centrally symmetric convex body.

Lassak, Marek (2008)

Beiträge zur Algebra und Geometrie

Beleuchtungsgebiete auf dem hyperbolischen Zylinder bei geometrischer Zentralbeleuchtung aus mehreren Lichtquellen

Mechthild Münch (1986)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Bemerkung über deltoidnahe" und ,, trapeznahe" asymmetrische Vierecke mit zwei einbeschriebenen Kreisen

KRÖTENHEERDT, K., P. RICHTER (1977)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Bemerkungen zur Definition einer erweiterten Affinoberfläche von E. Lutwak.

Kurt Leichtweiß (1989)

Manuscripta mathematica

Best constants for the isoperimetric inequality in quantitative form

Marco Cicalese, Gian Paolo Leonardi (2013)

Journal of the European Mathematical Society

We prove some results in the context of isoperimetric inequalities with quantitative terms. In the $2$ -dimensional case, our main contribution is a method for determining the optimal coefficients $c_{1}, ..., c_{m}$ in the inequality $δ P (E) \geq \sum_{k = 1}^{m} c_{k} α {(E)}^{k} + o (α {(E)}^{m})$ , valid for each Borel set $E$ with positive and finite area, with $δ P (E)$ and $α (E)$ being, respectively, the $𝑖𝑠𝑜𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑟𝑖𝑐𝑑𝑒𝑓𝑖𝑐𝑖𝑡$ and the $𝐹𝑟𝑎𝑒𝑛𝑘𝑒𝑙𝑎𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑦$ of $E$ . In $n$ dimensions, besides proving existence and regularity properties of minimizers for a wide class of $𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑎𝑡𝑖𝑣𝑒𝑖𝑠𝑜𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑟𝑖𝑐𝑞𝑢𝑜𝑡𝑖𝑒𝑛𝑡𝑠$ including the lower semicontinuous extension of $\frac{δ P (E)}{α {(E)}^{2}}$ , we describe the...

Bestimmung konvexer Körper durch Krümmungsmaße.

Rolf Schneider (1979)

Commentarii mathematici Helvetici

Between Paouris concentration inequality and variance conjecture

B. Fleury (2010)

Annales de l'I.H.P. Probabilités et statistiques

We prove an almost isometric reverse Hölder inequality for the euclidean norm on an isotropic generalized Orlicz ball which interpolates Paouris concentration inequality and variance conjecture. We study in this direction the case of isotropic convex bodies with an unconditional basis and the case of general convex bodies.

Bi- $(φ, ψ)$ convex sets.

Duca, D.I., Lupşa, L. (2003)

Mathematica Pannonica

Bisectors in Minkowski 3-space.

Horváth, Á.G. (2004)

Beiträge zur Algebra und Geometrie

Borsuk-Ulam type theorems

Adam Idzik (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

A generalization of the theorem of Bajmóczy and Bárány which in turn is a common generalization of Borsuk's and Radon's theorem is presented. A related conjecture is formulated.

Boundary of the union of rectangles in the plane

Václav Medek (1983)

Aplikace matematiky

Given $n$ rectangles in a plane whose all sides belong to two perpendicular directions, an algorithm for the construction of the boundary of the union of those rectangles is shown in teh paper.

Currently displaying 1 – 18 of 18

Page 1

Displaying 1 – 18 of 18

Balancing vectors and convex bodies

Ball versus distance convexity of metric spaces.

Banach spaces which are semi-L-summands in their biduals.

Banach-Mazur distance of central sections of a centrally symmetric convex body.

Beleuchtungsgebiete auf dem hyperbolischen Zylinder bei geometrischer Zentralbeleuchtung aus mehreren Lichtquellen

Bemerkung über deltoidnahe" und ,, trapeznahe" asymmetrische Vierecke mit zwei einbeschriebenen Kreisen

Bemerkungen zur Definition einer erweiterten Affinoberfläche von E. Lutwak.

Best constants for the isoperimetric inequality in quantitative form

Bestimmung konvexer Körper durch Krümmungsmaße.

Between Paouris concentration inequality and variance conjecture

Bi- $(φ, ψ)$ convex sets.

Bisectors in Minkowski 3-space.

Borsuk-Ulam type theorems

Boundary of the union of rectangles in the plane

Bounded linear regularity, strong CHIP, and CHIP are distinct properties.

Bounding the Piercing Number.

Bounds for capacities in terms of asymmetry.

Bounds of the affine breadth eccentricity of convex bodies via semi-infinite optimization.

Currently displaying 1 – 18 of 18