The supremum of conformally covariant eigenvalues in a conformal class

Details The supremum of conformally covariant eigenvalues in a conformal class The supremum of conformally covariant eigenvalues in a conformal class

2007-08-03

arxiv.org/abs/0708.0529v1

Mathematics

Differential Geometry

Scientific paper

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.

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