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r-Harmonic and Complex Isoparametric Functions on the Lie Groups Rm⋉ Rn and Rm⋉ H 2n+1

Gudmundsson, Sigmundur LU and Sobak, Marko (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.

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author
and
organization
publishing date
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
0232-704X
DOI
10.1007/s10455-020-09736-3
language
English
LU publication?
yes
id
4358bd9c-0a31-4f4a-8cd4-aacca3166cbc
date added to LUP
2020-10-28 09:15:42
date last changed
2021-02-10 16:52:49
@article{4358bd9c-0a31-4f4a-8cd4-aacca3166cbc,
  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         = {0232-704X},
  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},
}