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arXiv · 1712.03870

A Liouville-type theorem for biharmonic maps between complete Riemannian manifolds with small energies

Volker Branding
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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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Volker Branding. 2018-05-14. A Liouville-type theorem for biharmonic maps between complete Riemannian manifolds with small energies. https://doi.org/10.1007/s00013-018-1189-6

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