The second Yamabe invariant

Bernd Ammann (1) , Emmanuel Humbert (1)

1 IECN - Institut Élie Cartan de Nancy

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.

Domaines: Géométrie différentielle [math.DG]

Bernd Ammann, Emmanuel Humbert. The second Yamabe invariant. Journal of Functional Analysis, 2006, 235, pp.377-412. ⟨hal-00140807⟩