Bernd Ammann et Pierre Jammes, « The supremum of conformally covariant eigenvalues in a conformal class », in Variational Problems in Differential Geometry (ed. Bielawski, Houston et Speight), Vol. 394 de London Mathematical Society Lecture Note Series, p. 1-23, 2011, arXiv:0708.0529.
Mots clefs :
diraquien, laplacien conforme, valeurs propres conformes, opérateurs
conformément covariants.
Abstract:
Let (M,g) be a compact Riemannian manifold of dimension >=3.
We show that there are metrics g' 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 >=2.
Keywords:
Dirac operator, conformal Laplacian, conformal eigenvalues, conformally
covariant operators.
MSC2000 : 58C40, 58J50, 53A30.