Journal of the
Korean Mathematical Society JKMS

In this paper, we introduce the notion of the generalized symphonic map with respect to the functional $\Phi_\varepsilon$. Then we use the stress-energy tensor to obtain some monotonicity formulas and some Liouville results for these maps. We also obtain some Liouville type results by assuming some conditions on the asymptotic behavior of the maps at infinity.

Keywords: the generalized symphonic map, monotonicity formula, Liouville theorems

MSC numbers: 35B53, 58E20, 53C21

Supported by: This work was supported by the National Natural Science Foundation of China (11201400), Nanhu Scholars Program for Young Scholars of XYNU and the Universities Young Teachers Program of Henan Province (2016GGJS-096)