A New Approach to Lie Symmetry Groups of Minimal Surfaces

Publication Year:
2004
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Repository URL:
https://scholarsarchive.byu.edu/etd/321; https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=1320&context=etd
Author(s):
Berry, Robert D.
Publisher(s):
Brigham Young University - Provo
Tags:
minimal surfaces; Lie groups; harmonic; associated family; symmetry; geometric function theory; Mathematics
thesis / dissertation description
The Lie symmetry groups of minimal surfaces by way of planar harmonic functions are determined. It is shown that a symmetry group acting on the minimal surfaces is isomorphic with H × H^2 — the analytic functions and the harmonic functions. A subgroup of this gives a generalization of the associated family which is examined.