Isoperimetric profile comparisons and Yamabe constants

Abstract

We estimate from below the isoperimetric profile of $S^2 \times \re^2$ and use this information to obtain lower bounds for the Yamabe constant of $S^2 \times \re^2$. This provides a lower bound for the Yamabe invariants of products $S^2\times M^2$ for any closed Riemann surface $M$. Explicitly we show that $Y(S^2\times M^2)>(2/3)Y(S^4)$.

References in corpus (1)

• 3-Manifolds with Yamabe invariant greater than that of $\RP^3$