An Extension of Milman's Reverse Brunn-Minkowski Inequality.
An extension of the isoperimetric inequality on the sphere.
An inequality for convex curves in the plane.
An Inequality for the Volume of Inscribed Ellipsoids.
An isomorphic Dvoretzky's theorem for convex bodies
We prove that there exist constants C>0 and 0 < λ < 1 so that for all convex bodies K in with non-empty interior and all integers k so that 1 ≤ k ≤ λn/ln(n+1), there exists a k-dimensional affine subspace Y of satisfying . This formulation of Dvoretzky’s theorem for large dimensional sections is a generalization with a new proof of the result due to Milman and Schechtman for centrally symmetric convex bodies. A sharper estimate holds for the n-dimensional simplex.
An overview of semi-infinite programming theory and related topics through a generalization of the alternative theorems.
We propose new alternative theorems for convex infinite systems which constitute the generalization of the corresponding to Gale, Farkas, Gordan and Motzkin. By means of these powerful results we establish new approaches to the Theory of Infinite Linear Inequality Systems, Perfect Duality, Semi-infinite Games and Optimality Theory for non-differentiable convex Semi-Infinite Programming Problem.
An upper bound for a sequence of cevian inequalities.
Approximating 3-dimensional convex bodies by polytopes with a restricted number of edges.
Approximation of Convex Discs by Polygons.
Approximation of spherical caps by polygons
Approximation of the Euclidean ball by polytopes
There is a constant c such that for every n ∈ ℕ, there is an Nₙ so that for every N≥ Nₙ there is a polytope P in ℝⁿ with N vertices and where B₂ⁿ denotes the Euclidean unit ball of dimension n.
Around the Rogers-Shepard inequality.
Asphericity of shadows of a convex body.
Autour de l'inégalité de Brunn-Minkowski