Liouville type theorem for p-harmonic maps II
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Let M be a complete Riemannian manifold and let N be a Riemannian manifold of non-positive sectional curvature. Assume that RicM ≥ − 4(p−1) / p2 μ0 at all x ∈ M and Vol(M) is infinite, where μ0 > 0 is the infimum of the spectrum of the Laplacian acting on L2-functions on M. Then any p-harmonic map Φ : M → N of finite p-energy is constant. Also, we study Liouville type theorem for p-harmonic morphism.
Abstract
Let M be a complete Riemannian manifold and let N be a Riemannian manifold of non-positive sectional curvature. Assume that RicM ≥ − 4(p−1) / p2 μ0 at all x ∈ M and Vol(M) is infinite, where μ0 > 0 is the infimum of the spectrum of the Laplacian acting on L2-functions on M. Then any p-harmonic map Φ : M → N of finite p-energy is constant. Also, we study Liouville type theorem for p-harmonic morphism.
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