  For any closed Riemannian manifold $X$ we prove that large isoperimetric
regions in $X\times{\mathbb R}^n$ are of the form $X\times$(Euclidean ball). We
prove that if $X$ has non-negative Ricci curvature then the only soap bubbles
enclosing a large volume are the products $X\times$(Euclidean sphere). We give
an example of a surface $X$, with Gaussian curvature negative somewhere, such
that the product $X\times{\mathbb R}$ contains stable soap bubbles of
arbitrarily large enclosed volume which do not even project surjectively onto
the $X$ factor.
