Abstract
We estimate explicit lower bounds for the isoperimetric profiles of the Riemannian product of a compact manifold and the Euclidean space with the flat metric, (Mm×Rn,g+gE), m,n>1. In particular, we introduce a lower bound for the isoperimetric profile of Mm×Rn for regions of large volume and we improve on previous estimates of lower bounds for the isoperimetric profiles of S2×R2, S3×R2, S2×R3. We also discuss some applications of these results in order to improve known lower bounds for the Yamabe invariant of certain product manifolds.
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