Minimal Submanifolds via Complex-Valued Eigenfunctions

DOI10.1007/S12220-024-01642-5MaRDI QIDQ6497003

Sigmundur Gudmundsson, Thomas Jack Munn

Publication date: 6 May 2024

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Mathematics Subject Classification ID

Differential geometric aspects of harmonic maps (53C43) Harmonic maps, etc. (58E20) Differential geometry of symmetric spaces (53C35)

Cites Work

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• Harmonic maps from surfaces to complex projective spaces
• Harmonic morphisms from the classical compact semisimple Lie groups
• Harmonic morphisms from the classical non-compact semisimple Lie groups
• Harmonic maps into Lie groups (classical solutions of the chiral model)
• Twistor theory for Riemannian symmetric spaces. With applications to harmonic maps of Riemann surfaces
• \(p\)-harmonic maps and minimal submanifolds
• Harmonic two-spheres in compact symmetric spaces, revisited
• Biharmonic functions on the classical compact simple Lie groups
• A class of complete minimal submanifolds and their associated families of genuine deformations
• The Weierstrass representation for complete minimal real Kaehler submanifolds of codimension two
• Explicit proper \(p\)-harmonic functions on the Riemannian symmetric spaces \(\mathbf{SU} (n)/\mathbf{SO} (n)\), \(\mathbf{Sp} (n)/\mathbf{U} (n)\), \(\mathbf{SO} (2n)/\mathbf{U} (n)\), \(\mathbf{SU} (2n)/\mathbf{Sp} (n)\)
• Proper \(r\)-harmonic functions from Riemannian manifolds
• Minimal immersions of surfaces in Euclidean spheres
• The classical theory of minimal surfaces
• Harmonic Mappings of Riemannian Manifolds
• Explicit harmonic morphisms and \(p\)-harmonic functions from the complex and quaternionic Grassmannians
• Explicit \(p\)-harmonic functions on the real Grassmannians

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