Kenney, Joseph Patrick2009-11-182009-11-182009-08https://hdl.handle.net/11299/55076University of Minnesota Ph.D. dissertation. August 2009. Major: Mathematics. Advisor: Peter John Olver. 1 computer file (PDF); iv, 92 pages. Ill. (some col.)In this thesis we use the curve shortening flow along with a novel method of comparing differential invariant signatures to compare curves. We also look at what we can learn about Invariant curve flows from the evolution of differential invariant signatures.en-USDiffereintial InvariantsThesis or Dissertation