The second Yamabe invariant

摘要

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. (c) 2005 Elsevier Inc. All rights reserved.