Numerically Invariant Solutions of Geometric Flows
   
   Mireille Boutin
   Department of Mathematics
   University of Minnesota
   www.math.umn.edu/~mboutin

   Email:  mboutin@math.umn.edu

   Abstract:

Given a G-invariant differential equation (e.g. a geometric flow), we are
interested in obtaining numerical solution schemes which are also invariant
under G.  For example, we would like to obtain affine invariant numerical
schemes for the affine invariant flow C_t = Css for a curve C in the plane.  We
do this using an algorithmic method based on moving frames.  The method
involves solving a set of equations defining a cross-section of the orbits of
the group action.