The Dirac operator on untrapped surfaces

Simon Raulot (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We establish a sharp extrinsic lower bound for the first eigenvalue of the Dirac operator of an untrapped surface in initial data sets without apparent horizon in terms of the norm of its mean curvature vector. The equality case leads to rigidity results for the constraint equations with spherical boundary as well as uniqueness results for constant mean curvature surfaces in Minkowski space.

Mots clés: Dirac operator; Spectrum; Einstein equations; Rigidity

Domaines: Géométrie différentielle [math.DG]

Simon Raulot. The Dirac operator on untrapped surfaces. Communications in Mathematical Physics, 2013, 318 (2), pp.411-427. ⟨10.1007/s00220-013-1673-6⟩. ⟨hal-00632713⟩