The supremum of conformally covariant eigenvalues in a conformal class

Abstract

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.

References in corpus (4)

• Conformally invariant powers of the Laplacian, Q-curvature, and tractor calculus
• Sobolev spaces on Lie manifolds and regularity for polyhedral domains
• The first conformal Dirac eigenvalue on 2-dimensional tori
• The smallest Dirac eigenvalue in a spin-conformal class and cmc-immersions

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• A new upper bound for the Dirac operator on hypersurfaces
• Extremal Eigenvalues Of The Conformal Laplacian Under Sire-Xu Normalization