Isoperimetric estimates in low dimensional Riemannian products

Abstract

Euclidean space with the flat metric. We compute the isoperimetric profile of (T 2 × R n , h 2 + g E ), 2 ≤ n ≤ 5, for small and big values of the volume. These computations give explicit lower bounds for the isoperimetric profile of T 2 × R n . We also note that similar estimates for (We compute this explicitly for k = 3. We use symmetrization techniques for product manifolds, based on work of A. Ros ([19]) and F. Morgan ([10]).