The Journal of Geometric Analysis

, Volume 28, Issue 2, pp 1525–1547 | Cite as

Biharmonic Functions on the Classical Compact Simple Lie Groups

  • Sigmundur Gudmundsson
  • Stefano Montaldo
  • Andrea Ratto


The main aim of this work is to construct several new families of proper biharmonic functions defined on open subsets of the classical compact simple Lie groups \(\mathbf{SU}(n)\), \(\mathbf{SO}(n)\) and \(\mathbf{Sp}(n)\). We work in a geometric setting which connects our study with the theory of submersive harmonic morphisms. We develop a general duality principle and use this to interpret our new examples on the Euclidean sphere \({\mathbb S}^3\) and on the hyperbolic space \({\mathbb H}^3\).


Laplace-Beltrami operator Biharmonic functions Polyharmonic functions Lie groups 

Mathematics Subject Classification

58E20 31A30 35R03 



Work partially supported by: PRID 2015 – Università degli Studi di Cagliari.


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Copyright information

© Mathematica Josephina, Inc. 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceUniversity of LundLundSweden
  2. 2.Dipartimento di Matematica e InformaticaUniversità degli Studi di CagliariCagliariItaly
  3. 3.Dipartimento di Matematica e InformaticaUniversità degli Studi di CagliariCagliariItaly

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