On the Yamabe constants of S2 x R3 and S3 x R2

We compare the isoperimetric profiles of S-2 x R-3 and of S-3 x R-2 with that of a round 5-sphere (of appropriate radius). Then we use this comparison to obtain lower bounds for the Yamabe constants of S-2 x R-3 and S-3 x R-2. Explicitly we show that Y(S-3 x R-2, [g(0)(3) + dx(2)]) > (3/4)Y(S-5) and Y(S-2 x R-3, [g(2)(0) + dx(2)]) > 0.63Y(S-5). We also obtain explicit lower bounds in higher dimensions and for products of Euclidean space with a closed manifold of positive Ricci curvature. The techniques are a more general version of those used by the same authors in Petean and Ruiz (2011) [15] and the results are a complement to the work developed by B. Ammann, M. Dahl and E. Humbert to obtain explicit gap theorems for the Yamabe invariants in low dimensions. (C) 2013 Elsevier B.V. All rights reserved.