The second Yamabe invariant

Let (M, g) be a compact Riemannian manifold of dimension n 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. © 2005 Elsevier Inc. All rights reserved.