It is shown how one can draw graphs on surfaces of negative Euler characteristic by using hyperbolic geometry and hyperbolic circle packing representations. The same approach applies to drawings of hyperbolic tessellations.

In the field of Geometric Function Theory, one can not deny the importance of analytic and univalent functions. The characteristics of these functions including their taylor series expansion, their coefficients in these representations as well as their associated functional inequalities have always attracted the researchers. In particular, Fekete-Szegö inequality is one of such vastly studied a...

Arithmetic groups are a rich class of groups where connections between topology and number theory are showcased in a particularly striking way. One construction of these groups is motivated by the modular group, PSL2(Z). The group of orientation preserving isometries of the hyperbolic upper half plane, H, is isomorphic to PSL2(R). Since Z is a discrete subgroup of R it follows that PSL2(Z) is d...

This paper investigates hyperbolic polynomials with quasianalytic coefficients. Our main purpose is to prove factorization theorems for such polynomials, and next to generalize the results of K. Kurdyka and L. Paunescu about perturbation of analytic families of symmetric matrices to the quasianalytic settings. Generally, the perturbation problem concerns the issue whether, given a family of mon...