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

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