r-Harmonic and complex isoparametric functions on the Lie groups Rm⋉Rn and Rm⋉H2n+1
(2020) In Annals of Global Analysis and Geometry 58(4). p.477-496- Abstract
In this paper we introduce the notion of complex isoparametric functions on Riemannian manifolds. These are then employed to devise a general method for constructing proper r-harmonic functions. We then apply this to construct the first known explicit proper r-harmonic functions on the Lie group semidirect products Rm⋉ Rn and Rm⋉ H 2n+1, where H 2n+1 denotes the classical (2 n+ 1) -dimensional Heisenberg group. In particular, we construct such examples on all the simply connected irreducible four-dimensional Lie groups.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3d8a0e7b-f75f-4839-8a24-7e9398c145ca
- author
- Gudmundsson, Sigmundur
LU
and Sobak, Marko
- organization
- publishing date
- 2020-11-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Biharmonic functions, Solvable Lie groups
- in
- Annals of Global Analysis and Geometry
- volume
- 58
- issue
- 4
- pages
- 20 pages
- publisher
- Springer
- external identifiers
-
- scopus:85091254678
- ISSN
- 1572-9060
- DOI
- 10.1007/s10455-020-09736-3
- language
- English
- LU publication?
- yes
- id
- 3d8a0e7b-f75f-4839-8a24-7e9398c145ca
- date added to LUP
- 2020-10-09 14:08:09
- date last changed
- 2025-04-04 15:41:50
@article{3d8a0e7b-f75f-4839-8a24-7e9398c145ca, abstract = {{<p>In this paper we introduce the notion of complex isoparametric functions on Riemannian manifolds. These are then employed to devise a general method for constructing proper r-harmonic functions. We then apply this to construct the first known explicit proper r-harmonic functions on the Lie group semidirect products R<sup>m</sup>⋉ R<sup>n</sup> and R<sup>m</sup>⋉ H <sup>2</sup><sup>n</sup><sup>+</sup><sup>1</sup>, where H <sup>2</sup><sup>n</sup><sup>+</sup><sup>1</sup> denotes the classical (2 n+ 1) -dimensional Heisenberg group. In particular, we construct such examples on all the simply connected irreducible four-dimensional Lie groups.</p>}}, author = {{Gudmundsson, Sigmundur and Sobak, Marko}}, issn = {{1572-9060}}, keywords = {{Biharmonic functions; Solvable Lie groups}}, language = {{eng}}, month = {{11}}, number = {{4}}, pages = {{477--496}}, publisher = {{Springer}}, series = {{Annals of Global Analysis and Geometry}}, title = {{r-Harmonic and complex isoparametric functions on the Lie groups R<sup>m</sup>⋉R<sup>n</sup> and R<sup>m</sup>⋉H<sup>2</sup><sup>n</sup><sup>+</sup><sup>1</sup>}}, url = {{http://dx.doi.org/10.1007/s10455-020-09736-3}}, doi = {{10.1007/s10455-020-09736-3}}, volume = {{58}}, year = {{2020}}, }