Riesz continuity of the Atiyah
- 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.
| Author details: | Lashi BandaraORCiD, Alan McIntosh, Andreas Rosen |
|---|---|
| DOI: | https://doi.org/10.1007/s00208-017-1610-7 |
| ISSN: | 0025-5831 |
| ISSN: | 1432-1807 |
| Title of parent work (English): | Mathematische Annalen |
| Subtitle (English): | singer dirac operator under perturbations of the metric |
| Publisher: | Springer |
| Place of publishing: | Heidelberg |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2017/11/09 |
| Publication year: | 2017 |
| Release date: | 2022/02/04 |
| Volume: | 370 |
| Issue: | 1-2 |
| Number of pages: | 53 |
| First page: | 863 |
| Last Page: | 915 |
| Funding institution: | Knut and Alice Wallenberg foundationKnut & Alice Wallenberg Foundation [KAW 2013.0322]; Mathematical Sciences Institute at The Australian National University; Chalmers University of Technology; University of Gothenburg; Australian Research CouncilAustralian Research Council; Swedish Research Council, VRSwedish Research Council [621-2011-3744] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Green Open-Access |
