1 citations · 1 across the 3 of their papers we have counts for
3 papers
math.DG2008★ 1 cited
The Ricci flow does not preserve the set of Zoll metrics
Dan Jane
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 answ…
math.DS2007
On the injectivity of the X-ray transform for Anosov thermostats
Dan Jane, Gabriel P. Paternain
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 tran…
math.DS2006
An example of how the Ricci Flow can increase topological entropy
Dan Jane
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 app…