TY  - JOUR
A1  - Bandara, Lashi
A1  - McIntosh, Alan
A1  - Rosen, Andreas
T1  - Riesz continuity of the Atiyah
BT  - singer dirac operator under perturbations of the metric
JF  - Mathematische Annalen
N2  - We prove that the Atiyah–Singer Dirac operator in L2 depends Riesz continuously on L∞ perturbations of complete metrics g on a smooth manifold. The Lipschitz bound for the map depends on bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius. Our proof uses harmonic analysis techniques related to Calderón’s first commutator and the Kato square root problem. We also show perturbation results for more general functions of general Dirac-type operators on vector bundles.
Y1  - 2017
U6  - https://doi.org/10.1007/s00208-017-1610-7
SN  - 0025-5831
SN  - 1432-1807
VL  - 370
IS  - 1-2
SP  - 863
EP  - 915
PB  - Springer
CY  - Heidelberg
ER  -