Remarks on the nonexistence of biharmonic maps

DOI10.1007/s00013-016-0924-0zbMath1355.58005arXiv1511.07231OpenAlexW2963243169MaRDI QIDQ304074

Yong Luo

Publication date: 23 August 2016

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

Full work available at URL: https://arxiv.org/abs/1511.07231

zbMATH Keywords

harmonic mapnonpositive curvaturebiharmonic maptension fieldbioenergy functional

Mathematics Subject Classification ID

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

Related Items (7)

Biharmonic holomorphic maps into Kähler manifolds ⋮ A Liouville-type theorem for biharmonic maps between complete Riemannian manifolds with small energies ⋮ Nonexistence of proper \(p\)-biharmonic maps and Liouville type theorems. I: Case of \(p\ge 2\) ⋮ Unnamed Item ⋮ A nonexistence theorem for proper biharmonic maps into general Riemannian manifolds ⋮ Some remarks on bi-\(f\)-harmonic maps and \(f\)-biharmonic maps ⋮ \(F\)-biharmonic maps into general Riemannian manifolds

Cites Work

• Liouville-type theorems on complete manifolds and non-existence of bi-harmonic maps
• Conformal and semi-conformal biharmonic maps
• Biharmonic maps and morphisms from conformal mappings
• A mapping of Riemannian manifolds which preserves harmonic functions
• Harmonic morphisms between 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
• Harmonic Mappings of Riemannian Manifolds
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