On a smooth complete Riemannian spin manifold with smooth compact boundary,
we demonstrate that the Atiyah-Singer Dirac operator DB
in L2 depends Riesz continuously on L∞
perturbations of local boundary conditions B. The Lipschitz bound
for the map B→DB(1+DB2)−21 depends on Lipschitz smoothness
and ellipticity of B and bounds on Ricci curvature and its first
derivatives as well as a lower bound on injectivity radius. More generally, we
prove perturbation estimates for functional calculi of elliptic operators on
manifolds with local boundary conditions.Comment: Final versio