51 research outputs found
On the number of optimal surfaces
Let X be a closed oriented Riemann surface of genus > 1 of constant negative
curvature -1. A surface containing a disk of maximal radius is an optimal
surface. This paper gives exact formulae for the number of optimal surfaces of
genus > 3 up to orientation-preserving isometry. We show that the automorphism
group of such a surface is always cyclic of order 1,2,3 or 6. We also describe
a combinatorial structure of nonorientable hyperbolic optimal surfaces.Comment: This is the version published by Geometry & Topology Monographs on 29
April 200
Polyhedra with specified links
We construct compact polyhedra with -gonal faces whose links are
generalized 3-gons. It gives examples of cocompact hyperbolic bildings of type
. For we get compact spaces covered by Euclidean buildings of
type
Triangular hyperbolic buildings
We construct triangular hyperbolic polyhedra whose links are generalized
4-gons. The universal cover of those polyhedra are hyperbolic buildings, which
appartments are hyperbolic planes tesselated by regular triangles with angles
. Moreover, the fundamental groups of the polyhedra acts simply
transitively on vertices of the buildings
Series of -groups with Beauville structure
For every we show that each finite -group with an unmixed
Beauville structure is part of a surjective infinite projective system of
finite -groups with compatible unmixed Beauville structures. This leads to
the new notion of an unmixed topological Beauville structure on pro-finite
groups. We further construct for a new explicit infinite series of
non-abelian -groups that allow unmixed Beauville structures.Comment: 7 pages, to appear in: Monatshefte der Mathemati
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