Isoperimetric inequalities in convex cylinders and cylindrically bounded convex bodies

In this paper we consider the isoperimetric profile of convex cylinders $K\times {\mathbb{R}}^q$, where $K$ is an $m$-dimensional convex body, and of cylindrically bounded convex sets, i.e, those with a relatively compact orthogonal projection over some hyperplane of ${\mathbb{R}}^{n+1}$, asymptotic to a right convex cylinder of the form $K\times \mathbb{R}$, with $K\subset {\mathbb{R}}^n$. Results concerning the concavity of the isoperimetric profile, existence of isoperimetric regions, and geometric descriptions of isoperimetric regions for small and large volumes are obtained.