Biharmonic functions on the classical compact simple Lie groups

DOI10.1007/s12220-017-9877-1zbMath1414.58011arXiv1608.08391OpenAlexW2962927223WikidataQ115376800 ScholiaQ115376800MaRDI QIDQ1651379

Stefano Montaldo, Andrea Ratto, Sigmundur Gudmundsson

Publication date: 12 July 2018

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

Full work available at URL: https://arxiv.org/abs/1608.08391

zbMATH Keywords

Lie groupsLaplace-Beltrami operatorpolyharmonic functionsbiharmonic functions

Mathematics Subject Classification ID

Harmonic maps, etc. (58E20) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Related Items (13)

Biharmonic functions on spheres and hyperbolic spaces ⋮ Biharmonic functions on the special unitary group SU(2) ⋮ New biharmonic functions on the compact Lie groups \(\mathbf{SO}(n)\), \(\mathbf{SU}(n)\), \(\mathbf{Sp}(n)\) ⋮ A note on the Almansi property ⋮ Proper \(r\)-harmonic functions on the Thurston geometries ⋮ Explicit harmonic morphisms and \(p\)-harmonic functions from the complex and quaternionic Grassmannians ⋮ Explicit \(p\)-harmonic functions on the real Grassmannians ⋮ \(r\)-harmonic and complex isoparametric functions on the Lie groups \(\mathbb{R}^m\ltimes\mathbb{R}^n\) and \(\mathbb{R}^m\times\text{H}^{2n+1}\) ⋮ Bi-Lipschitz characteristic of quasiconformal self-mappings of the unit disk satisfying bi-harmonic equation ⋮ Explicit \(p\)-harmonic functions on rank-one Lie groups of Iwasawa type ⋮ Proper \(r\)-harmonic functions from Riemannian manifolds ⋮ Schwarz-type lemma, Landau-type theorem, and Lipschitz-type space of solutions to inhomogeneous biharmonic equations ⋮ Explicit proper \(p\)-harmonic functions on the Riemannian symmetric spaces \(\mathbf{SU} (n)/\mathbf{SO} (n)\), \(\mathbf{Sp} (n)/\mathbf{U} (n)\), \(\mathbf{SO} (2n)/\mathbf{U} (n)\), \(\mathbf{SU} (2n)/\mathbf{Sp} (n)\)

Cites Work

• Complete minimal submanifolds of compact Lie groups
• Harmonic morphisms from the classical compact semisimple Lie groups
• Biharmonic maps and morphisms from conformal mappings
• Minimal submanifolds of hyperbolic spaces via harmonic morphisms
• Harmonic morphisms from the Grassmannians and their non-compact duals
• \(p\)-harmonic morphisms, biharmonic morphisms, and nonharmonic biharmonic maps
• On the geometry of harmonic morphisms
• Lie groups beyond an introduction
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