Geometry, Topology and Dynamics Seminar
Andrew Sanders
UIC
A new proof of Bowen's theorem on the Hausdorff dimension of quasi-circles
Abstract: A quasi-Fuchsian group is a discrete group of Mobius transformations of the Riemann sphere which is isomorphic to the
fundamental group of a compact surface and acts properly on the complement of a Jordan curve: the limit set.
In 1979, Bowen proved a remarkable rigidity theorem on the Hausdorff dimension of the limit set of a quasi-Fuchsian
group: it is equal to 1 if and only if the limit set is a round circle. This theorem now has many generalizations. We will
present a new proof of Bowen's result as a by-product of a new lower bound on the Hausdorff dimension of the
limit set of a quasi-Fuchsian group. This lower bound is in terms of the differential geometric data of a immersed, $\pi_1$-injective
minimal surface in the quotient hyperbolic 3-manifold.
Monday September 9, 2013 at 3:00 PM in SEO 636