@article{BandaraMcIntoshRosen2017,
  author    = {Bandara, Lashi and McIntosh, Alan and Rosen, Andreas},
  title     = {Riesz continuity of the Atiyah},
  series = {Mathematische Annalen},
  volume    = {370},
  journal   = {Mathematische Annalen},
  number    = {1-2},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {0025-5831},
  doi       = {10.1007/s00208-017-1610-7},
  pages     = {863 -- 915},
  year      = {2017},
  abstract  = {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 Calder{\´o}n'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.},
  language  = {en}
}
@article{BandaraRosen2019,
  author    = {Bandara, Menaka Lashitha and Rosen, Andreas},
  title     = {Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions},
  series = {Communications in partial differential equations},
  volume    = {44},
  journal   = {Communications in partial differential equations},
  number    = {12},
  publisher = {Taylor \& Francis Group},
  address   = {Philadelphia},
  issn      = {0360-5302},
  doi       = {10.1080/03605302.2019.1611847},
  pages     = {1253 -- 1284},
  year      = {2019},
  abstract  = {On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that Atiyah-Singer Dirac operator in depends Riesz continuously on perturbations of local boundary conditions The Lipschitz bound for the map depends on Lipschitz smoothness and ellipticity of 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.},
  language  = {en}
}
@misc{BandaraRosen2019,
  author    = {Bandara, Menaka Lashitha and Ros{\´e}n, Andreas},
  title     = {Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions},
  series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  number    = {758},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-43407},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-434078},
  pages     = {1253 -- 1284},
  year      = {2019},
  abstract  = {On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that Atiyah-Singer Dirac operator in depends Riesz continuously on perturbations of local boundary conditions The Lipschitz bound for the map depends on Lipschitz smoothness and ellipticity of 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.},
  language  = {en}
}