Lower bounds for the eigenvalues of the spin\(^{c}\) Dirac-Witten operator
The author derives optimal lower bounds for the eigenvalues of the spin\(^c\) Dirac-Witten operator on spin\(^c\) space-like hypersurfaces in an \((n+1)\)-dimensional Lorentzian manifold. These estimates involve the mean curvature, the scalar curvature, the first eigenvalue of the perturbed Yamabe operator, and the spinorial energy-momentum tensor. Other limiting cases involving conformal lower bounds, and compact hypersurfaces with non-empty boundary are discussed. Contents include: Introduction; Preliminaries; Lower bounds for the eigenvalues; Conformal lower bounds; Compact hypersurfaces with non-empty boundary, and References (twenty-six items).
scientific article; zbMATH DE number 6019639
scientific article