Geodesic
A Liouville theorem for \(F\)-harmonic maps with finite \(F\)-energy
Electronic journal of differential equations, Tome 2006 (2006)
Let $(M,g)$ be a $m$-dimensional complete Riemannian manifold with a pole, and $(N,h)$ a Riemannian manifold. Let $F : \mathbb{R}^{+}\to \mathbb{R}^{+} $ be a strictly increasing $C^{2}$ function such that $F(0)=0$ and $F$-harmonic map $ u : M\to N$ with finite $F$-energy (i.e a local extremal of $E_{F}(u):= \int_{M} F(\vert du\vert^{2}/2)dV_{g}$ and $E_{F}(u)$ is finite) is a constant map provided that the radial curvature of $M$ satisfies a pinching condition depending to $d_{F}$.
Classification : 58E20, 53C21, 58J05
Keywords: F-harmonic maps, Liouville propriety, Stokes formula, comparison theorem 
@article{EJDE_2006__2006__a76,
     author = {Kassi,  M'hamed},
     title = {A {Liouville} theorem for {\(F\)-harmonic} maps with finite {\(F\)-energy}},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1089.58009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a76/}
}
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Kassi,  M'hamed. A Liouville theorem for \(F\)-harmonic maps with finite \(F\)-energy. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a76/