On embeddability of cones in euclidean spaces

On the Embeddability of Weighted Graphs in Euclidean Spaces

Embeddability of L1(μ) in dual spaces, geometry of cones and a characterization of c0

In this article we suppose that (Ω,Σ,μ) is a measure space and T an one-to-one, linear, continuous operator of L1(μ) into the dual E ′ of a Banach space E. For any measurable set A consider the image T (L1 (μA)) of the positive cone of the space L1(μA) in E′, where μA is the restriction of the measure μ on A. We provide geometrical conditions on the cones T (L1 (μA)) which yield that the measur...

On Polar Cones and Differentiability in Reflexive Banach Spaces

Let $X$ be a  Banach  space, $Csubset X$  be  a  closed  convex  set  included  in  a well-based cone $K$, and also let $sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a  bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set  $C$,  so that ${mathop{rm int}}(mathrm{dom} sigma_C) neqem...

Testing Embeddability Between Metric Spaces

Let L ≥ 1, > 0 be real numbers, (M,d) be a finite metric space and (N, ρ) be a metric space (Rudin 1976). The metric space (M,d) is said to be Lbilipschitz embeddable into (N, ρ) if there is an injective function f :M → N with 1/L · d(x, y) ≤ ρ(f(x), f(y)) ≤ L · d(x, y) for all x, y ∈ N (Farb & Mosher 1999, David & Semmes 2000, Croom 2002). In this paper, we also say that (M,d) is -far from bei...

On quasiplanes in Euclidean spaces

A variational inequality for the images of k-dimensional hyper-planes under quasiconformal maps of the n-dimensional Euclidean space is proved when 1 ≤ k ≤ n − 2 .