Proper \(r\)-harmonic submanifolds into ellipsoids and rotation hypersurfaces

DOI10.1016/j.na.2018.03.002zbMath1402.58014OpenAlexW2791705459MaRDI QIDQ1748239

Stefano Montaldo, Andrea Ratto

Publication date: 9 May 2018

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2018.03.002

zbMATH Keywords

harmonic mapsChen's conjecture\(r\)-harmonic immersions\(r\)-harmonic maps

Mathematics Subject Classification ID

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

Related Items (10)

Unique continuation properties for polyharmonic maps between Riemannian manifolds ⋮ Higher order energy functionals and the Chen-Maeta conjecture ⋮ Triharmonic CMC hypersurfaces in space forms with at most \(3\) distinct principal curvatures ⋮ Polyharmonic hypersurfaces into space forms ⋮ Triharmonic CMC hypersurfaces in \({\mathbb{R}}^5(c)\) ⋮ Some classifications of conformal biharmonic and \(k\)-polyharmonic maps ⋮ Higher order energy functionals ⋮ Triharmonic hypersurfaces with constant mean curvature in pseudo-Riemannian space forms ⋮ On polyharmonic helices in space forms ⋮ The stress-energy tensor for polyharmonic maps

Cites Work

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• The principle of symmetric criticality
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• New examples of \(r\)-harmonic immersions into the sphere
• A general approach to equivariant biharmonic maps
• The second variational formula of the \(k\)-energy and \(k\)-harmonic curves
• Biharmonic submanifolds into ellipsoids
• Rotationally symmetric biharmonic maps between models
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• BIHARMONIC CURVES INTO QUADRICS
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• HARMONIC MAPS BETWEEN SPHERES AND ELLIPSOIDS
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• Harmonic Mappings of Riemannian Manifolds
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