SYMMETRIZED TALAGRAND INEQUALITIES ON EUCLIDEAN SPACES

Isoperimetric Inequalities of Euclidean Type in Metric Spaces

1.1. Statement of the main result. The isoperimetric problem of euclidean type for a space X and given classes Ik−1, Ik, and Ik+1 of surfaces of dimension k − 1, k, and k + 1 in X , together with boundary operators Ik+1 ∂ −→ Ik ∂ −→ Ik−1 and a volume function M on each class, asks the following: Does there exist for every surface T ∈ Ik without boundary, ∂T = 0, a surface S ∈ Ik+1 with ∂S = T a...

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 .

On Isometries of Euclidean Spaces

Metric Derivations on Euclidean and Non-euclidean Spaces

As introduced by Weaver, (metric) derivations extend the notion of differential operators on Euclidean spaces and provide a linear differentiation theory that is well-defined on all metric spaces with Borel measures. The main result of this paper is a rigidity theorem for measures on Euclidean spaces that support a maximal number of derivations. The proof relies substantially on ideas from geom...

Gauge Theories on Noncommutative Euclidean Spaces

We consider gauge theories on noncommutative euclidean space . In particular, we discuss the structure of gauge group following standard mathematical definitions and using the ideas of hep-th/0102182 . AMS classification: 81T13, 81T75 The goal of this note is to consider gauge theories on noncommutative euclidean space and, in particular, to study the structure of gauge group. This group was an...