Some classifications of \infty-Harmonic maps between Riemannian manifolds

Details Some classifications of \infty-Harmonic maps between Riemannian manifolds Some classifications of \infty-Harmonic maps between Riemannian manifolds

2007-10-30

arxiv.org/abs/0710.5752v1

Mathematics

Differential Geometry

25 pages

Scientific paper

$\infty$-Harmonic maps are a generalization of $\infty$-harmonic functions. They can be viewed as the limiting cases of p-harmonic maps as p goes to infinity. In this paper, we give complete classifications of linear and quadratic $\infty$-harmonic maps from and into a sphere, quadratic $\infty$-harmonic maps between Euclidean spaces. We describe all linear and quadratic $\infty$-harmonic maps between Nil and Euclidean spaces, between Sol and Euclidean spaces. We also study holomorphic $\infty$-harmonic maps between complex Euclidean spaces.

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