Almost harmonic spinors

Zusammenfassung

We show that any closed spin manifold not diffeomorphic to the two-sphere admits a sequence of volume-one-Riemannian metrics for which the smallest non-zero Dirac eigenvalue tends to zero. As an application, we compare the Dirac spectrum with the conformal volume. (C) 2010 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.