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arXiv · 1010.3642

Isoperimetric profile comparisons and Yamabe constants

Jimmy Petean·Juan Miguel Ruiz
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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 $Y(S^2 \times M^2) > (2/3) Y(S^4)$.

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Jimmy Petean, Juan Miguel Ruiz. 2010-10-18. Isoperimetric profile comparisons and Yamabe constants. https://arxiv.org/abs/1010.3642

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