Ahlfors Bers Colloquium

May 19-22, 2005
University of Michigan
Ann Arbor, Michigan

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University of Michigan

Mathematics Department

Organizers
Dick Canary
Juha Heinonen

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Workshop Abstract Detail

Petra Bonfert-Taylor Wesleyan University

On the quasiconformal homogeneity of hyperbolic surfaces with fixed-point full automorphisms A hyperbolic manifold is $K$-quasiconformally homogeneous if for any two points in the manifold there exists a $K$-quasiconformal automorphism of the manifold mapping one point onto the other. Key in this definition is the existence of a bound $K$ on the dilatation which is independent of the pair of points in question. In dimensions three and above, rigidity phenomena make it possible to give a complete topological characterization of quasiconformally homogeneous hyperbolic manifolds. In this talk, we focus on the surface case. For example, we show that there exists a constant $K_{hyp}>1$ such that any $K$-quasiconformally homogeneous hyperelliptic surface satisfies that $K\geq K_{hyp}$.

Topic: Conformal Analysis and Geometric Function Theory