| |
| Dirac-harmonic map is the mathematical version of the super-symmetric nonlinear sigma model in quantum field theory, it includes the two important special cases: harmonic map and harmonic spinor. Many progresses have been made in the existence, regularity, blowup analysis, etc.. Most of the previous results deal with Dirac-harmonic maps from compact manifolds, it is the main aim of the present paper to derive properties of Dirac-harmonic maps from non-compact complete manifolds. Precisely, the authors established gradient estimates for Dirac-harmonic maps from non-compact complete Riemannian spin manifolds into regular balls of the target manifolds, and then apply these estimates to obtain Liouville theorems for Dirac-harmonic maps under certain conditions of the curvatures or energies, especially, they proved Liouville theorems of Dirac-harmonic maps under small energy density conditions. |
|
| Keywords:Pure Mathematical; Dirac-harmonic map; Liouvilletheorem; gradient estimate; noncompact manifolds |
|
