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The second Yamabe invariant

Bernd Ammann·Emmanuel Humbert
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Abstract

Let $(M,g)$ be a compact Riemannian manifold of dimension $n \geq 3$. We define the second Yamabe invariant as the infimum of the second eigenvalue of the Yamabe operator over the metrics conformal to $g$ and of volume 1. We study when it is attained. As an application, we find nodal solutions of the Yamabe equation.

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Bernd Ammann, Emmanuel Humbert. 2005-03-15. The second Yamabe invariant. https://arxiv.org/abs/math/0502094

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