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 S 2 × M 2 for any closed Riemann surface M. Explicitly we show that Y (S 2 × M 2) > (2/3)Y(S 4).
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Petean, J., Ruiz, J.M. Isoperimetric profile comparisons and Yamabe constants. Ann Glob Anal Geom 40, 177–189 (2011). https://doi.org/10.1007/s10455-011-9252-6
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DOI: https://doi.org/10.1007/s10455-011-9252-6