SPINOR PAIRS AND THE CONCENTRATION PRINCIPLE FOR DIRAC OPERATORS

摘要

We study perturbed Dirac operators of the form D-s = D + sA : Gamma(E) -> Gamma(F) over a compact Riemannian manifold (X, g) with symbol c and special bundle maps A : E -> F for s 0. Under a simple algebraic criterion on the pair (c, A), solutions of D-s psi = 0 concentrate as s -> infinity around the singular set Z(A) subset of X of A. We give many examples, the most interesting ones arising from a general " spinor pair" construction.