A new proof of Bowen’s theorem on Hausdorff dimension of quasi-circles
speaker: Andrew Sanders (University of Illinois, Chicago)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 an immersed, incompressible minimal surface in the quotient manifold. If time permits, generalizations of this result to other convex co-compact surface groups will be presented.
timetable:
Mon 9 Jun, 14:30 - 15:30, Aula Dini
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