[Spineurs presque harmoniques]
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.
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.
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@article{CRMATH_2010__348_13-14_811_0,
author = {Ginoux, Nicolas and Grosjean, Jean-Fran\c{c}ois},
title = {Almost harmonic spinors},
journal = {Comptes Rendus. Math\'ematique},
pages = {811--814},
publisher = {Elsevier},
volume = {348},
number = {13-14},
year = {2010},
doi = {10.1016/j.crma.2010.06.010},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.06.010/}
}
TY - JOUR AU - Ginoux, Nicolas AU - Grosjean, Jean-François TI - Almost harmonic spinors JO - Comptes Rendus. Mathématique PY - 2010 SP - 811 EP - 814 VL - 348 IS - 13-14 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.06.010/ DO - 10.1016/j.crma.2010.06.010 LA - en ID - CRMATH_2010__348_13-14_811_0 ER -
%0 Journal Article %A Ginoux, Nicolas %A Grosjean, Jean-François %T Almost harmonic spinors %J Comptes Rendus. Mathématique %D 2010 %P 811-814 %V 348 %N 13-14 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.06.010/ %R 10.1016/j.crma.2010.06.010 %G en %F CRMATH_2010__348_13-14_811_0
Ginoux, Nicolas; Grosjean, Jean-François. Almost harmonic spinors. Comptes Rendus. Mathématique, Tome 348 (2010) no. 13-14, pp. 811-814. doi : 10.1016/j.crma.2010.06.010. http://www.numdam.org/articles/10.1016/j.crma.2010.06.010/
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