Description:
We study boundary value problems for the Dirac operator on Riemannian Spinc manifolds of bounded geometry and with noncompact boundary. This generalizes a part of the theory of boundary value problems by C. Bar and W. Ballmann for complete manifolds with closed boundary. As an application, we derive the lower bound of Hijazi-Montiel-Zhang, involving the mean curvature of the boundary, for the spectrum of the Dirac operator on the noncompact boundary of a Spinc manifold. The limiting case is then studied and examples are then given.