r-Harmonic and Complex Isoparametric Functions on the Lie Groups R^m⋉R^n and R^m⋉H^(2n+1)
(2020) In Annals of Global Analysis and Geometry 58. 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 R^m⋉R^n and Rm⋉H^(2n+1), where H^(2n+1) denotes the classical (2n+1)-dimensional Heisenberg group. In particular, we construct such examples on all the simply connected irreducible four-dimensional Lie groups.
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https://lup.lub.lu.se/record/3d8a0e7b-f75f-4839-8a24-7e9398c145ca
- author
- Gudmundsson, Sigmundur
LU
and Sobak, Marko
- organization
- publishing date
- 2020-09-21
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Biharmonic functions, Solvable Lie groups
- in
- Annals of Global Analysis and Geometry
- volume
- 58
- pages
- 20 pages
- publisher
- Springer
- ISSN
- 1572-9060
- language
- English
- LU publication?
- yes
- id
- 3d8a0e7b-f75f-4839-8a24-7e9398c145ca
- date added to LUP
- 2020-10-09 14:08:09
- date last changed
- 2021-04-04 22:28:12
@article{3d8a0e7b-f75f-4839-8a24-7e9398c145ca, 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 R^m⋉R^n and Rm⋉H^(2n+1), where H^(2n+1) denotes the classical (2n+1)-dimensional Heisenberg group. In particular, we construct such examples on all the simply connected irreducible four-dimensional Lie groups.}, author = {Gudmundsson, Sigmundur and Sobak, Marko}, issn = {1572-9060}, language = {eng}, month = {09}, pages = {477--496}, publisher = {Springer}, series = {Annals of Global Analysis and Geometry}, title = {r-Harmonic and Complex Isoparametric Functions on the Lie Groups R^m⋉R^n and R^m⋉H^(2n+1)}, volume = {58}, year = {2020}, }