# 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