The first eigenvalue of the Dirac operator in a conformal class
by
Bernd Ammann, Emmanuel Humbert
The first eigenvalue of the Dirac operator in a conformal class
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International Journal of Geometric Methods in Modern Physics Vol. 3, Nos. 5-6 (2006) 833-844
DOI 10.1142/S0219887806001533
Proceedings for the conference "Symmetry in Geometry and Physics", Rome, Sept 14-17, 2005
in honour of D. V. Alekseevsky
In this overview article, we study the first positive eigenvalue of the Dirac operator in a unit volume conformal class. In particular, we discuss the question whether the infimum is attained. In the first part, we explain the corresponding variational problem. In the following parts we discuss the relation to the spinorial mass endomorphism and an application to surfaces of constant mean curvature. The article also mentions some open problems and work in progress.
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The Paper was written on 5.1.2006
Last update 25.9.2006