Isoperimetric profile comparisons and Yamabe constants

Details Isoperimetric profile comparisons and Yamabe constants Isoperimetric profile comparisons and Yamabe constants

2010-10-18

arxiv.org/abs/1010.3642v1

Mathematics

Differential Geometry

Scientific paper

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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