Nonexistence of Stable Harmonic Maps To and From Certain Homogeneous Spaces and Submanifolds of Euclidean Space

DOI10.2307/2000133zbMath0588.58015OpenAlexW4246240331MaRDI QIDQ3715913

Shihshu Walter Wei, Ralph Howard

Publication date: 1986

Full work available at URL: https://doi.org/10.2307/2000133

zbMATH Keywords

symmetric spacesinstability of harmonic maps

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Harmonic maps, etc. (58E20) Differential geometry of symmetric spaces (53C35)

Related Items (16)

Regularity of \(p\)-energy minimizing maps and \(p\)-superstrongly unstable indices ⋮ On stable quasi-harmonic maps and Liouville type theorems ⋮ Instability of spheres with deformed Riemannian metrics ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Pinching and nonexistence of stable harmonic maps ⋮ Homotopy and homology vanishing theorems and the stability of stochastic flows ⋮ Bloch bundles, Marzari-Vanderbilt functional and maximally localized Wannier functions ⋮ The geometry of \(\Phi_{( 3 )}\)-harmonic maps ⋮ Nonexistence of stable discrete maps into some homogeneous spaces of nonnegative curvature ⋮ Liouville type theorems and stability of \(\Phi_{S,p}\)-harmonic maps ⋮ \(\Phi\)-harmonic maps and \(\Phi\)-superstrongly unstable manifolds ⋮ Stable harmonic 2-spheres in symmetric spaces ⋮ Stability of natural energy functionals at Riemannian subimmersions ⋮ On stable currents and positively curved hypersurfaces ⋮ Regularity of minimizing harmonic maps into \(S^ 4\), \(S^ 5\) and symmetric spaces

Cites Work

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• Maps of minimum energy from compact simply-connected Lie groups
• Some results on stable harmonic maps
• Infima of energy functionals in homotopy classes of mappings
• The existence of minimal immersions of 2-spheres
• On stable currents and their application to global problems in real and complex geometry
• The Second Variation Formula for Harmonic Mappings
• Harmonic Mappings of Riemannian Manifolds

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