Event time:
Monday, February 1, 2010 - 9:30am to 10:30am
Location:
431 DL
Speaker:
Daniel Thompson
Speaker affiliation:
Penn State
Event description:
In 2004, Manning showed that the topological entropy of the geodesic
flow for a surface of negative curvature decreases as the metric
evolves
under the normalised Ricci flow. It is an interesting open problem,
also due to Manning, to determine to what extent such behaviour
persists for higher
dimensional manifolds. I will describe a strong curvature condition on
the metric under which monotonicity of the topological entropy can be
established for a short time. In particular, this criterion applies to
metrics of negative sectional curvature which are in the same
conformal class as a metric of constant negative sectional curvature.