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Metabelian groups acting on compact Riemann surfaces.

G. Gromadzki (1995)

Revista Matemática de la Universidad Complutense de Madrid

A metabelian group G acting as automorphism group on a compact Riemann surface of genus g ≥ 2 has order less than or equal to 16(g-1). We calculate for which values of g this bound is achieved and on these cases we calculate a presentation of the group G.

Metric spaces nonembeddable into Banach spaces with the Radon-Nikodým property and thick families of geodesics

Mikhail I. Ostrovskii (2014)

Fundamenta Mathematicae

We show that a geodesic metric space which does not admit bilipschitz embeddings into Banach spaces with the Radon-Nikodým property does not necessarily contain a bilipschitz image of a thick family of geodesics. This is done by showing that no thick family of geodesics is Markov convex, and comparing this result with results of Cheeger-Kleiner, Lee-Naor, and Li. The result contrasts with the earlier result of the author that any Banach space without the Radon-Nikodým property contains a bilipschitz...

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