The supremum of conformally covariant eigenvalues in a conformal class

Bernd Ammann (1) , Pierre Jammes (2)

1 IECN - Institut Élie Cartan de Nancy
2 LANLG - Laboratoire d'Analyse non linéaire et Géométrie

Let (M,g) be a compact Riemannian manifold of dimension >2. We show that there is a metric h conformal to g and of volume 1 such that the first positive eigenvalue the conformal Laplacian with repect to h is arbitrarily large. A similar statement is proven for the first positive eigenvalue of the Dirac operator on a spin manifold of dimension >1.

Domaines: Géométrie différentielle [math.DG]

Bernd Ammann, Pierre Jammes. The supremum of conformally covariant eigenvalues in a conformal class. 2007. ⟨hal-00166342⟩