Ana Portilla

A characterization of Gromov hyperbolicity of surfaces with variable negative curvature

In this paper we show that, in order to check Gromov hyperbolicity of any surface with curvature K≤ −k² < 0, we just need to verify the Rips condition on a very small class of triangles, namely, those contained in simple closed geodesics. This result is, in fact, a new characterization of Gromov hyperbolicity for this kind of surfaces.

THE ROLE OF FUNNELS AND PUNCTURES IN THE GROMOV HYPERBOLICITY OF RIEMANN SURFACES

We prove results on geodesic metric spaces which guarantee that some spaces are not hyperbolic in the Gromov sense. We use these theorems in order to study the hyperbolicity of Riemann surfaces. We obtain a criterion on the genus of a surface which implies the non-hyperbolicity. We also have a characterization of the hyperbolicity of a Riemann surface S∗ obtained by deleting a closed set from one original surface S. In the particular case when the closed set is a union of continua and isolated points, the results clarify the role of punctures and funnels (and other more general ends) in the hyperbolicity of Riemann surfaces. (1) Research partially supported by a grant from DGI (BFM 2003-04870), Spain. (2) Research partially supported by a grant from DGI (BFM 2000-0022), Spain.

Weierstrass' theorem with weights

We characterize the set of functions which can be approximated by continuous functions in the L∞ norm with respect to almost every weight. This allows to characterize the set of functions which can be approximated by polynomials or by smooth functions for a wide range of weights.

Zero location and asymptotic behavior for extremal polynomials with non-diagonal Sobolev norms

In this paper we are going to study the zero location and asymptotic behavior of extremal polynomials with respect to a non-diagonal Sobolev norm in the worst case, i.e., when the quadratic form is allowed to degenerate. The orthogonal polynomials with respect to this Sobolev norm are a particular case of those extremal polynomials. The multiplication operator by the independent variable is the main tool in order to obtain our results.

Comparative Gromov hyperbolicity results for the hyperbolic and quasihyperbolic metrics

In this article, we investigate the Gromov hyperbolicity of Denjoy domains equipped with the hyperbolic or the quasihyperbolic metric. The focus are on comparative or decomposition results, which allow us to reduce the question of whether a given domain is Gromov hyperbolic to a series of questions concerning simpler domains. We also give several concrete examples of applications of the results.

Planarity and Hyperbolicity in Graphs

If X is a geodesic metric space and

Gromov Hyperbolicity in Mycielskian Graphs

x_1,x_2,x_3

Gromov hyperbolicity through decomposition of metrics spaces II

x1,x2,x3 are three points in