Riesz continuity of the Atiyah–Singer Dirac operator under perturbations of local boundary conditions
Artikel i vetenskaplig tidskrift, 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+/D2B)−12 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 away from a compact neighbourhood of the boundary. More generally, we prove perturbation estimates for functional calculi of elliptic operators on manifolds with local boundary conditions.

Dirac operator

Boundary value problems

functional calculus

Riesz continuity

spectral flow

real-variable harmonic analysis


Lashi Bandara

Universität Potsdam

Andreas Rosén

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Communications in Partial Differential Equations

0360-5302 (ISSN) 1532-4133 (eISSN)

Vol. 44 12 1253-1284




Matematisk analys



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