Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions

Autoren: Lashi Bandara, Andreas Rosén (2019)

On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that 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)-1/2 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.

Comm. Part. Diff. Eq.
Taylor & Francis
DOI: 10.1080/03605302.2019.1611847

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