%0 Journal Article
%T Soap bubbles and isoperimetric regions in the product of a closed manifold with Euclidean space
%A Jes¨˛s Gonzalo P¨Śrez
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1312.6311v1