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Complex-Valued Harmonic Morphisms and p-Harmonic Functions on Compact Riemannian Lie Groups

Zapata Sarmiento, Luis Miguel LU (2023) In Bachelor's Theses in Mathematical Sciences MATM03 20222
Mathematics (Faculty of Sciences)
Centre for Mathematical Sciences
Abstract
In this Master’s thesis, we describe two recent methods aimed at constructing
complex-valued harmonic morphisms and p-harmonic functions on Riemannian
manifolds. The main tools for these constructions are the common eigenfunctions
of the classical Laplace-Beltrami operator τ and the recently introduced conformality
operator κ. We then apply the above methods for constructing solutions on
the compact Lie groups SU(n), SO(n) and Sp(n), equipped with their respective
classical biinvariant Riemannian metrics.
Please use this url to cite or link to this publication:
author
Zapata Sarmiento, Luis Miguel LU
supervisor
organization
course
MATM03 20222
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Riemannian manifolds, harmonic functions, compact Lie groups, eigenfunctions, eigenfamilies.
publication/series
Bachelor's Theses in Mathematical Sciences
report number
LUNFMA-3134-2023
ISSN
1404-6342
other publication id
2023:E:11
language
English
id
9113761
date added to LUP
2025-06-12 15:48:42
date last changed
2025-06-12 15:48:42
@misc{9113761,
  abstract     = {{In this Master’s thesis, we describe two recent methods aimed at constructing
complex-valued harmonic morphisms and p-harmonic functions on Riemannian
manifolds. The main tools for these constructions are the common eigenfunctions
of the classical Laplace-Beltrami operator τ and the recently introduced conformality
operator κ. We then apply the above methods for constructing solutions on
the compact Lie groups SU(n), SO(n) and Sp(n), equipped with their respective
classical biinvariant Riemannian metrics.}},
  author       = {{Zapata Sarmiento, Luis Miguel}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Bachelor's Theses in Mathematical Sciences}},
  title        = {{Complex-Valued Harmonic Morphisms and p-Harmonic Functions on Compact Riemannian Lie Groups}},
  year         = {{2023}},
}