Dirac-harmonic maps from index theory

DOI10.1007/s00526-012-0534-zzbMath1275.58010arXiv1110.1309OpenAlexW2019846587MaRDI QIDQ353131

Bernd Ammann, Nicolas Ginoux

Publication date: 12 July 2013

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.1309

zbMATH Keywords

harmonic mapspin structureindex theoryDirac-harmonic mapfermionic energy functional

Mathematics Subject Classification ID

Index theory and related fixed-point theorems on manifolds (58J20) Spin and Spin({}^c) geometry (53C27) Differential geometric aspects of harmonic maps (53C43) Harmonic maps, etc. (58E20)

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Cites Work

• Nonlinear Dirac equations with critical nonlinearities on compact spin manifolds
• The spectrum of the twisted Dirac operator on Kähler submanifolds of the complex projective space
• Bubble tree convergence for harmonic maps
• A structure theorem of Dirac-harmonic maps between spheres
• Dirac-harmonic maps
• Energy identities for Dirac-harmonic maps
• Surgery and harmonic spinors
• Dirac-harmonic maps from degenerating spin surfaces. I: The Neveu-Schwarz case
• Some explicit constructions of Dirac-harmonic maps
• The existence of minimal immersions of 2-spheres
• Harmonic spinors on Riemann surfaces
• Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative Ricci curvature
• Applications harmoniques de surfaces riemanniennes
• Harmonic spinors for twisted Dirac operators
• Harmonic spinors
• Geometry of harmonic maps
• Regularity for weakly Dirac-harmonic maps to hypersurfaces
• Nonlinear Dirac equations on Riemann surfaces
• On the space of metrics with invertible Dirac operator
• Harmonic spinors and local deformations of the metric
• Metrics with harmonic spinors
• Regularity theorems and energy identities for Dirac-harmonic maps
• Liouville theorems for Dirac-harmonic maps
• Regularity of Dirac-Harmonic Maps
• Characteristic Classes. (AM-76)
• Surgery and the spectrum of the Dirac operator
• Harmonic Mappings of Riemannian Manifolds
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