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Journal articles on the topic 'Dirac-harmonic maps'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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1

Chen, Qun, Jürgen Jost, Jiayu Li, and Guofang Wang. "Dirac-harmonic maps." Mathematische Zeitschrift 254, no. 2 (May 25, 2006): 409–32. http://dx.doi.org/10.1007/s00209-006-0961-7.

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2

Branding, Volker. "Magnetic Dirac-harmonic maps." Analysis and Mathematical Physics 5, no. 1 (May 16, 2014): 23–37. http://dx.doi.org/10.1007/s13324-014-0081-1.

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3

Branding, Volker. "Dirac-harmonic maps with torsion." Communications in Contemporary Mathematics 18, no. 04 (May 3, 2016): 1550064. http://dx.doi.org/10.1142/s0219199715500649.

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We study Dirac-harmonic maps from surfaces to manifolds with torsion, which is motivated from the superstring action considered in theoretical physics. We discuss analytic and geometric properties of such maps and outline an existence result for uncoupled solutions.
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4

Jost, Jürgen, and Jingyong Zhu. "Existence of (Dirac-)harmonic Maps from Degenerating (Spin) Surfaces." Journal of Geometric Analysis 31, no. 11 (April 30, 2021): 11165–89. http://dx.doi.org/10.1007/s12220-021-00676-3.

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AbstractWe study the existence of harmonic maps and Dirac-harmonic maps from degenerating surfaces to a nonpositive curved manifold via the scheme of Sacks and Uhlenbeck. By choosing a suitable sequence of $$\alpha $$ α -(Dirac-)harmonic maps from a sequence of suitable closed surfaces degenerating to a hyperbolic surface, we get the convergence and a cleaner energy identity under the uniformly bounded energy assumption. In this energy identity, there is no energy loss near the punctures. As an application, we obtain an existence result about (Dirac-)harmonic maps from degenerating (spin) surfaces. If the energies of the map parts also stay away from zero, which is a necessary condition, both the limiting harmonic map and Dirac-harmonic map are nontrivial.
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5

Chen, Q., J. Jost, and G. Wang. "Liouville theorems for Dirac-harmonic maps." Journal of Mathematical Physics 48, no. 11 (November 2007): 113517. http://dx.doi.org/10.1063/1.2809266.

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6

Chen, Qun, Jürgen Jost, Linlin Sun, and Miaomiao Zhu. "Dirac-harmonic maps between Riemann surfaces." Asian Journal of Mathematics 23, no. 1 (2019): 107–26. http://dx.doi.org/10.4310/ajm.2019.v23.n1.a6.

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7

Ammann, Bernd, and Nicolas Ginoux. "Some examples of Dirac-harmonic maps." Letters in Mathematical Physics 109, no. 5 (October 30, 2018): 1205–18. http://dx.doi.org/10.1007/s11005-018-1134-4.

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8

Zhao, Liang. "Energy Identities for Dirac-harmonic Maps." Calculus of Variations and Partial Differential Equations 28, no. 1 (July 15, 2006): 121–38. http://dx.doi.org/10.1007/s00526-006-0035-z.

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9

Ammann, Bernd, and Nicolas Ginoux. "Dirac-harmonic maps from index theory." Calculus of Variations and Partial Differential Equations 47, no. 3-4 (June 21, 2012): 739–62. http://dx.doi.org/10.1007/s00526-012-0534-z.

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10

Liu, Lei. "No neck for Dirac-harmonic maps." Calculus of Variations and Partial Differential Equations 52, no. 1-2 (December 25, 2013): 1–15. http://dx.doi.org/10.1007/s00526-013-0702-9.

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11

Jost, Jürgen, Xiaohuan Mo, and Miaomiao Zhu. "Some explicit constructions of Dirac-harmonic maps." Journal of Geometry and Physics 59, no. 11 (November 2009): 1512–27. http://dx.doi.org/10.1016/j.geomphys.2009.07.011.

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12

Hamilton, M. J. D. "J-holomorphic curves and Dirac-harmonic maps." Differential Geometry and its Applications 68 (February 2020): 101587. http://dx.doi.org/10.1016/j.difgeo.2019.101587.

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13

Chen, Qun, Jürgen Jost, Guofang Wang, and Miaomiao Zhu. "The boundary value problem for Dirac-harmonic maps." Journal of the European Mathematical Society 15, no. 3 (2013): 997–1031. http://dx.doi.org/10.4171/jems/384.

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14

Zhu, Miaomiao. "Regularity for weakly Dirac-harmonic maps to hypersurfaces." Annals of Global Analysis and Geometry 35, no. 4 (November 13, 2008): 405–12. http://dx.doi.org/10.1007/s10455-008-9142-8.

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15

Isobe, Takeshi. "Asymptotically linear Dirac-harmonic maps into flat tori." Differential Geometry and its Applications 75 (April 2021): 101716. http://dx.doi.org/10.1016/j.difgeo.2020.101716.

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16

Chen, Qun, Jürgen Jost, and Linlin Sun. "Gradient estimates and Liouville theorems for Dirac-harmonic maps." Journal of Geometry and Physics 76 (February 2014): 66–78. http://dx.doi.org/10.1016/j.geomphys.2013.10.011.

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17

Branding, Volker. "Some aspects of Dirac-harmonic maps with curvature term." Differential Geometry and its Applications 40 (June 2015): 1–13. http://dx.doi.org/10.1016/j.difgeo.2015.01.008.

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18

Yang, Ling. "A structure theorem of Dirac-harmonic maps between spheres." Calculus of Variations and Partial Differential Equations 35, no. 4 (November 11, 2008): 409–20. http://dx.doi.org/10.1007/s00526-008-0210-5.

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19

Chen, Qun, Jürgen Jost, Jiayu Li, and Guofang Wang. "Regularity theorems and energy identities for Dirac-harmonic maps." Mathematische Zeitschrift 251, no. 1 (May 14, 2005): 61–84. http://dx.doi.org/10.1007/s00209-005-0788-7.

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20

Branding, Volker. "Nonlinear Dirac Equations, Monotonicity Formulas and Liouville Theorems." Communications in Mathematical Physics 372, no. 3 (November 13, 2019): 733–67. http://dx.doi.org/10.1007/s00220-019-03608-z.

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Abstract We study the qualitative behavior of nonlinear Dirac equations arising in quantum field theory on complete Riemannian manifolds. In particular, we derive monotonicity formulas and Liouville theorems for solutions of these equations. Finally, we extend our analysis to Dirac-harmonic maps with curvature term.
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21

Ai, Wanjun, and Miaomiao Zhu. "Regularity for Dirac-harmonic maps into certain pseudo-Riemannian manifolds." Journal of Functional Analysis 279, no. 7 (October 2020): 108633. http://dx.doi.org/10.1016/j.jfa.2020.108633.

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22

Chen, Qun, Jürgen Jost, and Guofang Wang. "The maximum principle and the Dirichlet problem for Dirac-harmonic maps." Calculus of Variations and Partial Differential Equations 47, no. 1-2 (March 29, 2012): 87–116. http://dx.doi.org/10.1007/s00526-012-0512-5.

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23

Zhu, Miaomiao. "Dirac-harmonic maps from degenerating spin surfaces I: the Neveu–Schwarz case." Calculus of Variations and Partial Differential Equations 35, no. 2 (August 15, 2008): 169–89. http://dx.doi.org/10.1007/s00526-008-0201-6.

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24

Jost, Jürgen, Lei Liu, and Miaomiao Zhu. "Energy identity for a class of approximate Dirac-harmonic maps from surfaces with boundary." Annales de l'Institut Henri Poincaré C, Analyse non linéaire 36, no. 2 (March 2019): 365–87. http://dx.doi.org/10.1016/j.anihpc.2018.05.006.

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25

Sun, Linlin. "A Note on the uncoupled Dirac-harmonic maps from Kähler spin manifolds to Kähler manifolds." manuscripta mathematica 155, no. 1-2 (June 2, 2017): 197–208. http://dx.doi.org/10.1007/s00229-017-0941-8.

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26

Jost, Jürgen, and Jingyong Zhu. "$$\alpha $$-Dirac-harmonic maps from closed surfaces." Calculus of Variations and Partial Differential Equations 60, no. 3 (May 11, 2021). http://dx.doi.org/10.1007/s00526-021-01955-1.

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Abstract$$\alpha $$ α -Dirac-harmonic maps are variations of Dirac-harmonic maps, analogous to $$\alpha $$ α -harmonic maps that were introduced by Sacks–Uhlenbeck to attack the existence problem for harmonic maps from closed surfaces. For $$\alpha >1$$ α > 1 , the latter are known to satisfy a Palais–Smale condition, and so, the technique of Sacks–Uhlenbeck consists in constructing $$\alpha $$ α -harmonic maps for $$\alpha >1$$ α > 1 and then letting $$\alpha \rightarrow 1$$ α → 1 . The extension of this scheme to Dirac-harmonic maps meets with several difficulties, and in this paper, we start attacking those. We first prove the existence of nontrivial perturbed $$\alpha $$ α -Dirac-harmonic maps when the target manifold has nonpositive curvature. The regularity theorem then shows that they are actually smooth if the perturbation function is smooth. By $$\varepsilon $$ ε -regularity and suitable perturbations, we can then show that such a sequence of perturbed $$\alpha $$ α -Dirac-harmonic maps converges to a smooth coupled $$\alpha $$ α -Dirac-harmonic map.
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27

Wang, C., and D. Xu. "Regularity of Dirac-Harmonic Maps." International Mathematics Research Notices, May 18, 2009. http://dx.doi.org/10.1093/imrn/rnp064.

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28

Jost, Jürgen, Lei Liu, and Miaomiao Zhu. "Regularity of Dirac-harmonic maps with $$\lambda $$-curvature term in higher dimensions." Calculus of Variations and Partial Differential Equations 58, no. 6 (October 13, 2019). http://dx.doi.org/10.1007/s00526-019-1632-y.

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Abstract In this paper, we will study the partial regularity for stationary Dirac-harmonic maps with $$\lambda $$λ-curvature term. For a weakly stationary Dirac-harmonic map with $$\lambda $$λ-curvature term $$(\phi ,\psi )$$(ϕ,ψ) from a smooth bounded open domain $$\Omega \subset {\mathbb {R}}^m$$Ω⊂Rm with $$m\ge 2$$m≥2 to a compact Riemannian manifold N, if $$\psi \in W^{1,p}(\Omega )$$ψ∈W1,p(Ω) for some $$p>\frac{2m}{3}$$p>2m3, we prove that $$(\phi , \psi )$$(ϕ,ψ) is smooth outside a closed singular set whose $$(m-2)$$(m-2)-dimensional Hausdorff measure is zero. Furthermore, if the target manifold N does not admit any harmonic sphere $$S^l$$Sl, $$l=2,\ldots , m-1$$l=2,…,m-1, then $$(\phi ,\psi )$$(ϕ,ψ) is smooth.
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29

Jost, Jürgen, Lei Liu, and Miaomiao Zhu. "Blow-up analysis for approximate Dirac-harmonic maps in dimension 2 with applications to the Dirac-harmonic heat flow." Calculus of Variations and Partial Differential Equations 56, no. 4 (July 10, 2017). http://dx.doi.org/10.1007/s00526-017-1202-0.

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30

Branding, Volker. "On the Evolution of Regularized Dirac-Harmonic Maps from Closed Surfaces." Results in Mathematics 75, no. 2 (March 18, 2020). http://dx.doi.org/10.1007/s00025-020-1178-5.

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31

Sharp, Ben, and Miaomiao Zhu. "Regularity at the free boundary for Dirac-harmonic maps from surfaces." Calculus of Variations and Partial Differential Equations 55, no. 2 (February 27, 2016). http://dx.doi.org/10.1007/s00526-016-0960-4.

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32

Liu, Lei, and Miaomiao Zhu. "Boundary Value Problems for Dirac-Harmonic Maps and Their Heat Flows." Vietnam Journal of Mathematics, April 1, 2021. http://dx.doi.org/10.1007/s10013-021-00484-w.

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33

Isobe, Takeshi. "On the multiple existence of superquadratic Dirac-harmonic maps into flat tori." Calculus of Variations and Partial Differential Equations 58, no. 4 (July 8, 2019). http://dx.doi.org/10.1007/s00526-019-1578-0.

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34

Li, Jiayu, Lei Liu, Chaona Zhu, and Miaomiao Zhu. "Energy identity and necklessness for $$\alpha $$-Dirac-harmonic maps into a sphere." Calculus of Variations and Partial Differential Equations 60, no. 4 (July 2, 2021). http://dx.doi.org/10.1007/s00526-021-02019-0.

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35

Wittmann, Johannes. "Short time existence of the heat flow for Dirac-harmonic maps on closed manifolds." Calculus of Variations and Partial Differential Equations 56, no. 6 (November 4, 2017). http://dx.doi.org/10.1007/s00526-017-1270-1.

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36

Jost, Jürgen, Lei Liu, and Miaomiao Zhu. "Asymptotic analysis for Dirac-harmonic maps from degenerating spin surfaces and with bounded index." Calculus of Variations and Partial Differential Equations 58, no. 4 (July 24, 2019). http://dx.doi.org/10.1007/s00526-019-1557-5.

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37

Jost, Jürgen, Lei Liu, and Miaomiao Zhu. "Correction to: Asymptotic analysis for Dirac-harmonic maps from degenerating spin surfaces and with bounded index." Calculus of Variations and Partial Differential Equations 58, no. 5 (September 25, 2019). http://dx.doi.org/10.1007/s00526-019-1617-x.

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