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Isoperimetric profile comparisons and Yamabe constants

2011; Springer Science+Business Media; Volume: 40; Issue: 2 Linguagem: Inglês

10.1007/s10455-011-9252-6

1572-9060

Jimmy Petean, Juan Miguel Ruiz,

Analytic and geometric function theory

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).