VIGRE at Rice: http://math.rice.edu/VIGRE
Our current research project.
Begin with a simple, closed, planar curve, C.
Let J(C) be the flatness energy of the curve,
J(C) = ∫ k2
Allow C to evolve by making local changes in order to minimize J.
We conjecture that C will evolve into a circle of infinite radius. We recall that k is the inverse of the radius, R, of the osculating circle, so k = 0 requires R = 8.
Currently, we are studying the behavior of curves under a "curve flattening" evolution.
Overviews of our past research projects.
Presentations and major findings.
Many thanks to the NSF and the VIGRE program at Rice University.