The Ricci flow does not preserve the set of Zoll metrics (2008)
The question of whether or not the set of Zoll metrics on the 2-sphere is connected is still open. Here we show that a naive application of the Ricci flow is not sufficient to answer this problem.
On the injectivity of the X-ray transform for Anosov thermostats (2007)
Jane, Dan, Paternain, Gabriel P.
We consider Anosov thermostats on a closed surface and the X-ray transform on functions which are up to degree two in the velocities. We show that the subspace where the X-ray transform fails to be...
An example of how the Ricci Flow can increase topological entropy (2006)
We give a surface for which the Ricci Flow applied to the metric will increase the topological entropy of the geodesic flow. Specifically, we first adapt the Melnikov method to apply to a Ricci Flow...