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

Abstract

Given a compact Riemannian manifold $M$ without boundary, we show that large isoperimetric regions in $M\times {\mathbb{R}}^k$ are tubular neighborhoods of $M\times \{x\}$, with $x\in {\mathbb{R}}^k$.

arXiv commentFinal version, to appear in Adv. Math

References in corpus (3)

• Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions
• Existence of isoperimetric regions in contact sub-Riemannian manifolds
• Soap bubbles and isoperimetric regions in the product of a closed manifold with Euclidean space

Cited by in corpus (2)

• Isoperimetric inequalities in convex cylinders and cylindrically bounded convex bodies
• Soap bubbles and isoperimetric regions in the product of a closed manifold with Euclidean space