Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of the metric
Journal article, 2018

We prove that the Atiyah-Singer Dirac operator D-g in L-2 depends Riesz continuously L-infinity on perturbations of complete metrics on a smooth manifold. The Lipschitz bound for the map g -> D-g(1 + D-g(2))(-1/2) 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 Caldern'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.


Lashi Bandara

University of Potsdam

Alan McIntosh

Australian National University

Andreas Rosén

University of Gothenburg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Mathematische Annalen

0025-5831 (ISSN) 1432-1807 (eISSN)

Vol. 370 1-2 863-915

Subject Categories

Computational Mathematics


Mathematical Analysis



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Latest update

5/3/2018 9