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 Liouville theorems for generalized symphonic maps J. Korean Math. Soc. 2019 Vol. 56, No. 3, 669-688 https://doi.org/10.4134/JKMS.j180297Published online May 1, 2019 Shuxiang Feng, Yingbo Han Southwest University; Xinyang Normal University Abstract : 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 Full-Text :