Cutoff on hyperbolic surfaces

Hyperbolic surfaces of $L_1$-2-type

In this paper, we show that an $L_1$-2-type surface in the three-dimensional hyperbolic space $H^3subset R^4_1$ either is an open piece of a standard Riemannian product $ H^1(-sqrt{1+r^2})times S^{1}(r)$, or it has non constant mean curvature, non constant Gaussian curvature, and non constant principal curvatures.

Complex networks on hyperbolic surfaces

We explore a novel method to generate and characterize complex networks by means of their embedding on hyperbolic surfaces. Evolution through local elementary moves allows the exploration of the ensemble of networks which share common embeddings and consequently share similar hierarchical properties. This method provides a new perspective to classify network-complexity both on local and global ...

Transitive Hyperbolic Sets on Surfaces

We show that every transitive hyperbolic set on a surface is included in a locally maximal hyperbolic set.

Identities on hyperbolic manifolds and quasiconformal homogeneity of hyperbolic surfaces

Lengths of Systoles on Tileable Hyperbolic Surfaces

The same triangle may tile geometrically distinct surfaces of the same genus, and these tilings may determine isomorphic tiling groups. We determine if there are geometric differences in the surfaces that can be found using group theoretic methods. Specifically, we determine if the systole, the shortest closed geodesic on a surface, can distinguish a certain families of tilings. For example, th...