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Research on Differential Geometry in Brazil
Some friends of mine insisted that I should present a personal account of research developments in Differential Geometry in Brazil at the lOth School...
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On the Blaschke conjecture for 3-webs
We find relative differential invariants of orders eight and nine for a planar nonparallelizable 3-web such that their vanishing is necessary and...
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Discrete and Convex Geometry
Mathematical research in Hungary started with geometry: with the work of the two Bolyais early in the 19th century. The father, Farkas Bolyai, showed...
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Error of Asymptotic Formulae for Volume Approximation of Convex Bodies in
We estimate the error of asymptotic formulae for volume approximation of sufficiently differentiable convex bodies by circumscribed convex polytopes...
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The “Full Müntz Theorem” inL p[0, 1] for 0<p<∞
Denote by span { f 1 , f 2 , …} the collection of all finite linear combinations of the functions f 1 , f 2 , … over ℝ. The principal result of the paper is...
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Volumes in High Dimension
We begin with comparing the volume of the n-dimensional cube with the volume of the unit ball inscribed in it, in order to realize that volumes of...
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Mahler’s conjecture and other transcendence Results
The first transcendental result about values of the modular invariant j (“if τ is algebraic but not imaginary quadratic then j(τ) is transcendental”)...
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Advances on Extremal Problems in Number Theory and Combinatorics
To keep an acceptable size, references not listed at the end are given by the Bibliography of the recent book [N] and/or the page number of [N].
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Nearly Umbilical Ovaloids in the n-Space are close to Spheres
An ovaloid F in the euclidean n -space ℝ n ( n ≧ 3) is called δ - umbilical (δ ≧ 0) if δ equals the L ∞ -norm, i.e. the maximum of the difference of the...
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Some conjectures aboutLp norms of k-plane transforms
For 1≤ k ≤ n -1, the k-plane transform T k,n carries functions f defined on R n to functions T k,n f defined on the set of affine k-planes in R n . It is known...
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Stability of Blaschke's Characterization of Ellipsoids and Radon Norms
Roughly speaking, in this article we prove quantitative versions of the following statements: (i) If each shadow boundary of a convex body in E ...
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Bonnesen-style inequalities and pseudo-perimeters for polygons
In this paper, we establish some Bonnesen-style isoperimetric inequalities for plane polygons via an analytic isoperimetric inequality and an...
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An improved asymptotic analysis of the expected number of pivot steps required by the simplex algorithm
Let a 1 ..., a m be i.i.d. points uniformly on the unit sphere in ℝ n , m ≥ n ≥ 3, and let X := { x ε ℝ n | a
i T x ≤1} be the random polyhedron generated by a 1 ... -
Finite Packing Problems
In n-dimensional Euclidean space, how should one arrange m nonoverlap** translates of a given convex body K in order to minimize the diameter, the...
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The Busemann-Petty Problem
The search for relationships between a convex body and its projections or sections has a long history. In 1841, A. Cauchy found that the surface area...