scholarly journals Gradient estimates and Liouville theorems for Dirac-harmonic maps

2014 ◽  
Vol 76 ◽  
pp. 66-78 ◽  
Author(s):  
Qun Chen ◽  
Jürgen Jost ◽  
Linlin Sun
Keyword(s):  
Harmonic Maps ◽  
Gradient Estimates ◽  
Liouville Theorems

scholarly journals Liouville theorems for Dirac-harmonic maps

2007 ◽  
Vol 48 (11) ◽  
pp. 113517 ◽  
Author(s):  
Q. Chen ◽  
J. Jost ◽  
G. Wang
Keyword(s):  
Harmonic Maps ◽  
Liouville Theorems

scholarly journals On VT-harmonic maps

2019 ◽  
Vol 57 (1) ◽  
pp. 71-94 ◽  
Author(s):  
Qun Chen ◽  
Jürgen Jost ◽  
Hongbing Qiu
Keyword(s):  
Maximum Principle ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Existence Results ◽  
Gradient Estimates ◽  
Hermitian Manifolds ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic System ◽  
Levi Civita Connection ◽  
Complete Manifolds

Abstract VT-harmonic maps generalize the standard harmonic maps, with respect to the structure of both domain and target. These can be manifolds with natural connections other than the Levi-Civita connection of Riemannian geometry, like Hermitian, affine or Weyl manifolds. The standard harmonic map semilinear elliptic system is augmented by a term coming from a vector field V on the domain and another term arising from a 2-tensor T on the target. In fact, this geometric structure then also includes other geometrically defined maps, for instance magnetic harmonic maps. In this paper, we treat VT-harmonic maps and their parabolic analogues with PDE tools. We establish a Jäger–Kaul type maximum principle for these maps. Using this maximum principle, we prove an existence theorem for the Dirichlet problem for VT-harmonic maps. As applications, we obtain results on Weyl/affine/Hermitian harmonic maps between Weyl/affine/Hermitian manifolds, as well as on magnetic harmonic maps from two-dimensional domains. We also derive gradient estimates and obtain existence results for such maps from noncompact complete manifolds.

scholarly journals Monotonicity formulae and Liouville theorems of harmonic maps with potential

2012 ◽  
Vol 62 (9) ◽  
pp. 1939-1948 ◽  
Author(s):  
Hezi Lin ◽  
Guilin Yang ◽  
Yibin Ren ◽  
Tian Chong
Keyword(s):  
Harmonic Maps ◽  
Liouville Theorems ◽  
Harmonic Maps With Potential
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