DreyfussA122009.pdf (249.71 kB)
The Mean Curvature Flow of Polar Action Orbits
thesis
posted on 2009-12-16, 00:00 authored by Andrew A DreyfussMean curvature flow describes the process by which a submanifold is deformed in the direction of its mean curvature vector. A polar action is noteworthy in this context because it admits complete submanifolds called sections that intersect each orbit orthogonally. The mean curvature vector of a polar orbit is tangent to this section, so the problem of solving for the flow of these orbits reduces to solving a system of ordinary dierential equations over a section. For this reason the symmetry properties of a section may be used to construct the possible flow lines and predict which points are invariant under the flow. The corresponding orbits are minimal submanifolds.
History
Date Created
2009-12-16Date Modified
2022-10-18Research Director(s)
Xiaobo LiuDegree
- Master of Science in Applied Mathematics
Degree Level
- Master's Thesis
Language
- English
Alternate Identifier
etd-12162009-132802Publisher
University of Notre DameProgram Name
- Mathematics
Usage metrics
Categories
No categories selectedLicence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC