New biharmonic functions on the compact Lie groups SO(n), SU(n), Sp(n)

Gudmundsson, Sigmundur; Siffert, Anna

doi:10.1007/s12220-019-00259-3

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

New biharmonic functions on the compact Lie groups SO(n), SU(n), Sp(n)

MPS-Authors

/persons/resource/persons248579

Gudmundsson, Sigmundur
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons236214

Siffert, Anna
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1007/s12220-019-00259-3
(Publisher version)

https://doi.org/10.48550/arXiv.1812.02777
(Preprint)

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

Gudmundsson-Siffert_New biharmonic functions on the compact Lie groups_2021.pdf
(Publisher version), 419KB

Supplementary Material (public)

There is no public supplementary material available

Citation

Gudmundsson, S., & Siffert, A. (2021). New biharmonic functions on the compact Lie groups SO(n), SU(n), Sp(n). The Journal of Geometric Analysis, 31(1), 250-281. doi:10.1007/s12220-019-00259-3.

Cite as: https://hdl.handle.net/21.11116/0000-0006-9E3F-3

Abstract

We develope a new scheme for the construction of explicit complex-valued
proper biharmonic functions on Riemannian Lie groups. We exploit this and
manufacture many infinite series of uncountable families of new solutions on
the special unitary group $SU(n)$. We then show that the special orthogonal
group $SO(n)$ and the quaternionic unitary group $Sp(n)$ fall into the scheme.
As a by-product we obtain new harmonic morphisms on these groups. All the
constructed maps are defined on open and dense subsets of the corresponding
spaces.