Almost harmonic spinors
نویسندگان
چکیده
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. Spineurs presque harmoniques Résumé. Nous montrons que, sur toute variété spinorielle compacte sans bord non difféomorphe à la sphère de dimension deux, il existe une suite de métriques riemanniennes de volume un pour laquelle la plus petite valeur propre non nulle de l’opérateur de Dirac tend vers zéro. Comme application, nous comparons le spectre de l’opérateur de Dirac avec le volume conforme.
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