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arXiv · 2306.06042

Lower bounds for isoperimetric profiles and Yamabe constants

Juan Miguel Ruiz·Areli Vázquez Juárez
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Abstract

We estimate explicit lower bounds for the isoperimetric profiles of the Riemannian product of a compact manifold and the Euclidean space with the flat metric, $(M^m\times \mathbb{R}^n,g+g_E)$, $m,n>1$. In particular, we introduce a lower bound for the isoperimetric profile of $M^m\times \mathbb{R}^n$ for regions of large volume and we improve on previous estimates of lower bounds for the isoperimetric profiles of $S^2 \times \mathbb{R}^2$, $S^3 \times \mathbb{R}^2$, $S^2 \times \mathbb{R}^3$. We also discuss some applications of these results in order to improve known lower bounds for the Yamabe invariant of certain manifolds.

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Juan Miguel Ruiz, Areli Vázquez Juárez. 2023-06-09. Lower bounds for isoperimetric profiles and Yamabe constants. https://arxiv.org/abs/2306.06042

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