Optimal eigenvalue estimate for the Dirac-Witten operator on bounded domains with smooth boundary

Daniel Maerten (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

Eigenvalue estimate for the Dirac-Witten operator is given on bounded domains (with smooth boundary) of spacelike hypersurfaces satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS, and chiral conditions). This result is a generalisation of Friedrich's inequality for the usual Dirac operator. The limiting cases are also investigated.

Mots clés: dominant energy condition

Mots clés: Dirac-Witten operator; eigenvalue; dominant energy condition.

Domaines: Géométrie différentielle [math.DG]

Daniel Maerten. Optimal eigenvalue estimate for the Dirac-Witten operator on bounded domains with smooth boundary. 2007. ⟨hal-00199521⟩