Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions
- 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.
| Author details: | Menaka Lashitha BandaraORCiD, Andreas RosenORCiD |
|---|---|
| DOI: | https://doi.org/10.1080/03605302.2019.1611847 |
| ISSN: | 0360-5302 |
| ISSN: | 1532-4133 |
| Title of parent work (English): | Communications in partial differential equations |
| Publisher: | Taylor & Francis Group |
| Place of publishing: | Philadelphia |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2019 |
| Publication year: | 2019 |
| Release date: | 2021/01/04 |
| Tag: | Boundary value problems; Dirac operator; Riesz continuity; functional calculus; real-variable harmonic analysis; spectral flow |
| Volume: | 44 |
| Issue: | 12 |
| Number of pages: | 32 |
| First page: | 1253 |
| Last Page: | 1284 |
| Funding institution: | Knut and Alice Wallenberg foundationKnut & Alice Wallenberg Foundation [KAW 2013.0322, SPP2026]; German Research Foundation (DFG)German Research Foundation (DFG) |
| 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 / Hybrid Open-Access |
| License (German): |  CC-BY - Namensnennung 4.0 International |
| External remark: | Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 758 |
