A Liouville-type theorem for biharmonic maps between complete Riemannian manifolds with small energies |
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Authors: | Volker Branding |
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Institution: | 1.Faculty of Mathematics,University of Vienna,Vienna,Austria |
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Abstract: | We prove a Liouville-type theorem for biharmonic maps from a complete Riemannian manifold of dimension \(n\) that has a lower bound on its Ricci curvature and positive injectivity radius into a Riemannian manifold whose sectional curvature is bounded from above. Under these geometric assumptions we show that if the \(L^p\)-norm of the tension field is bounded and the n-energy of the map is sufficiently small, then every biharmonic map must be harmonic, where \(2<p<n\). |
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