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- Bandara, L.Universität Potsdam,University of Potsdam (author)
Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of the metric
- Article/chapterEnglish2018
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- 2017-11-09
- Springer Science and Business Media LLC,2018
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- LIBRIS-ID:oai:gup.ub.gu.se/264131
- https://gup.ub.gu.se/publication/264131URI
- https://doi.org/10.1007/s00208-017-1610-7DOI
- https://research.chalmers.se/publication/500523URI
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- Language:English
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- We prove that the Atiyah-Singer Dirac operator D-g in L-2 depends Riesz continuously L-infinity on perturbations of complete metrics on a smooth manifold. The Lipschitz bound for the map g -> D-g(1 + D-g(2))(-1/2) 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 Caldern'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.
Subject headings and genre
- NATURVETENSKAP Matematik hsv//swe
- NATURAL SCIENCES Mathematics hsv//eng
- NATURVETENSKAP Matematik Beräkningsmatematik hsv//swe
- NATURAL SCIENCES Mathematics Computational Mathematics hsv//eng
- NATURVETENSKAP Matematik Geometri hsv//swe
- NATURAL SCIENCES Mathematics Geometry hsv//eng
- NATURVETENSKAP Matematik Matematisk analys hsv//swe
- NATURAL SCIENCES Mathematics Mathematical Analysis hsv//eng
- square-root problem
- adjoint fredholm operators
- spectral flow
- vector-bundles
- Mathematics
- intosh a
- 1972
- proceedings of the american mathematical society
- v32
- p430
Added entries (persons, corporate bodies, meetings, titles ...)
- McIntosh, A.Australian National University (author)
- Rosén, Andreas,1974Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology(Swepub:cth)rosenan (author)
- Universität PotsdamAustralian National University (creator_code:org_t)
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- In:Mathematische Annalen: Springer Science and Business Media LLC370:1-2, s. 863-9150025-58311432-1807
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