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Riesz continuity of...
Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of the metric
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- Bandara, L. (författare)
- Universität Potsdam,University of Potsdam
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- McIntosh, A. (författare)
- Australian National University
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- Rosén, Andreas, 1974 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology
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(creator_code:org_t)
- 2017-11-09
- 2018
- Engelska.
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Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 370:1-2, s. 863-915
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- 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)
Nyckelord
- square-root problem
- adjoint fredholm operators
- spectral flow
- vector-bundles
- Mathematics
- intosh a
- 1972
- proceedings of the american mathematical society
- v32
- p430
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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