# The supremum of conformally covariant eigenvalues in a conformal class

by

Bernd Ammann, Pierre Jammes

** The supremum of first eigenvalues of conformally covariant operators in a conformal class**
(.dvi, .ps,.ps.gz or .pdf)

in *Variational Problems in Differential Geometry,*

Proceedings of a Conference in Leeds on the occasion of J. Woods 60th birthday,

Leeds 2009, London Mathematical Society Lecture Notes Series
**394**, *1-23* (2011)

DOI: 10.1017/CBO9780511863219.002

Let (M,g) be a compact Riemannian manifold of dimension >2. We show that there are metrics h conformal to g and of volume 1 such that the first positive eigenvalue the conformal Laplacian 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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The Paper was written on July 26, 2007

Last update March 8, 2012