Isoperimetric profile comparisons and Yamabe constants

Abstract

We estimate from below the isoperimetric profile of \({S^2 \times {\mathbb R}^2}\) and use this information to obtain lower bounds for the Yamabe constant of \({S^2 \times {\mathbb R}^2}\) . This provides a lower bound for the Yamabe invariants of products S2 × M2 for any closed Riemann surface M. Explicitly we show that Y (S2 × M2) > (2/3)Y(S4).