The second Yamabe invariant

By Bernd Ammann, E. Humbert. 2005

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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.

Subfields: Applied Mathematics

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