Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of the metric

DOI10.1007/s00208-017-1610-7zbMath1384.58015arXiv1603.03647OpenAlexW2294302434MaRDI QIDQ681648

Lashi Bandara, Andreas Rosén, Alan G. R. McIntosh

Publication date: 12 February 2018

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.03647

zbMATH Keywords

Atiyah-Singer Dirac operatorperturbation of metricRiesz continuity

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Perturbations of PDEs on manifolds; asymptotics (58J37) Spectral flows (58J30) First-order elliptic systems (35J46) Harmonic analysis and PDEs (42B37)

Related Items

Schatten class estimates for the Riesz map of massless Dirac operators, Essential self-adjointness of powers of first-order differential operators on non-compact manifolds with low-regularity metrics, Functional calculus and harmonic analysis in geometry, Riesz continuity of the Atiyah–Singer Dirac operator under perturbations of local boundary conditions

Cites Work

• The Kato square root problem on vector bundles with generalised bounded geometry
• Quadratic estimates and functional calculi of perturbed Dirac operators
• The Dirac spectrum
• L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
• Spineurs, opérateurs de Dirac et variations de métriques. (Spinors, Dirac operators and variations of the metrics)
• The solution of the Kato square root problem for second order elliptic operators on \(\mathbb R^n\).
• Local Hardy spaces of differential forms on Riemannian manifolds
• The functional calculus for sectorial operators
• Index theory for skew-adjoint Fredholm operators
• Essential self-adjointness of powers of generators of hyperbolic equations
• BASIC FUNCTIONAL ANALYSIS PUZZLES OF SPECTRAL FLOW
• The Kato square root problem on submanifolds
• Density problems on vector bundles and manifolds
• Self-Adjoint Fredholm Operators And Spectral Flow
• A T(b) theorem with remarks on analytic capacity and the Cauchy integral
• Riemannian Geometry
• On the Comparability of A 1/2 and A ∗ 1/2
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