On the Lp Spectrum of the Dirac Operator.

Our main goal in the present paper is to expand the known class of noncompact manifolds over which the L 2 -spectrum of a general Dirac operator and its square is maximal. To achieve this, we first find sufficient conditions on the manifold so that the L p -spectrum of the Dirac operator and its square is independent of p for p ≥ 1 . Using the L 1 -spectrum, which is simpler to compute, we generalize the class of manifolds over which the L p -spectrum of the Dirac operator is the real line for all p. We also show that by applying the generalized Weyl criterion, we can find large classes of manifolds with asymptotically nonnegative Ricci curvature, or which are asymptotically flat, such that the L 2 -spectrum of a general Dirac operator and its square is maximal. [ABSTRACT FROM AUTHOR]