Isoperimetric inequalities in convex cylinders and cylindrically bounded convex bodies

Abstract

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.

22 pages. Final version to appear in Calc. Var. PDE

References in corpus (1)

• Large isoperimetric regions in the product of a compact manifold with Euclidean space

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