Optimal eigenvalues estimate for the Dirac operator on domains with boundary

Simon Raulot (1)

1 IECN - Institut Élie Cartan de Nancy

We give a lower bound for the eigenvalues of the Dirac operator on a compact domain of a Riemannian spin manifold under the $\MIT$ bag boundary condition. The limiting case is characterized by the existence of an imaginary Killing spinor.

Mots clés: Dirac Operator; Spectrum; Boundary condition; Ellipticity; Constant mean curvature hypersurfaces

Domaines: Géométrie différentielle [math.DG]

Simon Raulot. Optimal eigenvalues estimate for the Dirac operator on domains with boundary. Letters in Mathematical Physics, 2005, 73, pp.135--145. ⟨hal-00021463⟩