Geodesic
A Liouville theorem for $F$-harmonic maps with finite $F$-energy
Electronic Journal of Differential Equations, Tome 2006 (2006).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Kassi, M'hamed},
     title = {A {Liouville} theorem for $F$-harmonic maps with finite $F$-energy},
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     volume = {2006},
     year = {2006},
     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/