Quasiconformal Homogeneity after Gehring and Palka

Identities on hyperbolic manifolds and quasiconformal homogeneity of hyperbolic surfaces

A lower bound for Torelli-K-quasiconformal homogeneity

A closed hyperbolic Riemann surfaceM is said to beK-quasiconformally homogeneous if there exists a transitive family F of K-quasiconformal homeomorphisms. Further, if all [f ] ⊂ F act trivially on H1(M ;Z), we say M is Torelli-K-quasiconformally homogeneous. We prove the existence of a uniform lower bound on K for Torelli-K-quasiconformally homogeneous Riemann surfaces. This is a special case o...

Teichmüller Mappings, Quasiconformal Homogeneity, and Non-amenable Covers of Riemann Surfaces

We show that there exists a universal constant Kc so that every K-strongly quasiconformally homogeneous hyperbolic surface X (not equal to H2) has the property that K > Kc > 1. The constant Kc is the best possible, and is computed in terms of the diameter of the (2, 3, 7)-hyperbolic orbifold (which is the hyperbolic orbifold of smallest area.) We further show that the minimum strong homogeneity...

Walter Gehring (1939–2014)

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Walter Jakob Gehring (1939-2014)

Walter Jakob Gehring [3] discovered the homeobox [4], a DNA segment found in a specific cluster of genes [5] that determine the body plan of animals, plants, and fungi. Gehring identified the homeobox [4] in 1983, with the help of colleagues while isolating the Antennapedia (Antp) gene in fruit flies (Drosophila [6]) at the University of Basel [7] in Basel, Switzerland. Hox genes [8], a family ...