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

DOI10.1007/S00013-018-1189-6zbMath1400.58003arXiv1712.03870OpenAlexW2800551503WikidataQ115390089 ScholiaQ115390089MaRDI QIDQ1660102

Volker Branding

Publication date: 23 August 2018

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.03870

zbMATH Keywords

Liouville theorembiharmonic mapscomplete Riemannian manifolds

Mathematics Subject Classification ID

Differential geometric aspects of harmonic maps (53C43) Harmonic maps, etc. (58E20)

Related Items (9)

A vanishing result for the supersymmetric nonlinear sigma model in higher dimensions ⋮ On harmonic and biharmonic maps from gradient Ricci solitons ⋮ Some analytic results on interpolating sesqui-harmonic maps ⋮ A structure theorem for polyharmonic maps between Riemannian manifolds ⋮ The stress-energy tensor for polyharmonic maps ⋮ On finite energy solutions of 4-harmonic and ES-4-harmonic maps ⋮ A nonexistence theorem for proper biharmonic maps into general Riemannian manifolds ⋮ On interpolating sesqui-harmonic maps between Riemannian manifolds ⋮ \(F\)-biharmonic maps into general Riemannian manifolds

Cites Work

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• Liouville-type theorems on complete manifolds and non-existence of bi-harmonic maps
• Remarks on the nonexistence of biharmonic maps
• Sobolev spaces on Riemannian manifolds
• Biharmonic maps into a Riemannian manifold of non-positive curvature
• Biharmonic maps from a complete Riemannian manifold into a non-positively curved manifold
• A special Stoke's theorem for complete Riemannian manifolds
• Liouville-type theorems for biharmonic maps between Riemannian manifolds
• On Liouville’s Theorem for Biharmonic Functions

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