The talk deals with boundary value problems for dirac type operators on a complete Riemannian manifold with compact boundary. After a short introduction to Dirac operators on Riemanian manifolds, suitable boundary conditions to ensure Fredholm property of the involved operators will be introduced. Some results concerning index calculation and spectral theory for these operators will be discussed.
Bär, Ballmann: Guide to boundary value problems for Dirac-type operators,
Boundary value problems for elliptic differential operators of first order