Coarse embedding into uniformly convex Banach spaces

Abstract

In this paper, the author studies the coarse embedding into uniformly convex Banach spaces. The author proves that the property of coarse embedding into Banach spaces can be preserved under taking the union of the metric spaces under certain conditions. As an application, for a group G strongly relatively hyperbolic to a subgroup H, the author proves that B(n) = {g ∈ G | |g|S∪ℋ ≤ n} admits a coarse embedding into a uniformly convex Banach space if H does.