منابع مشابه
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 non-hyperbolicity. We also include a characterization of the hyperbolicity of a Riemann surface S∗ obtained by deleting a closed set from on...
متن کاملDetours and Gromov hyperbolicity
The notion of Gromov hyperbolicity was introduced by Gromov in the setting of geometric group theory [G1], [G2], but has played an increasing role in analysis on general metric spaces [BHK], [BS], [BBo], [BBu], and extendability of Lipschitz mappings [L]. In this theory, it is often additionally assumed that the hyperbolic metric space is proper and geodesic (meaning that closed balls are compa...
متن کاملGromov Hyperbolicity in Mycielskian Graphs
Since the characterization of Gromov hyperbolic graphs seems a too ambitious task, there are many papers studying the hyperbolicity of several classes of graphs. In this paper, it is proven that every Mycielskian graph GM is hyperbolic and that δ(GM) is comparable to diam(GM). Furthermore, we study the extremal problems of finding the smallest and largest hyperbolicity constants of such graphs;...
متن کاملGromov Invariants for Holomorphic Maps from Riemann Surfaces to Grassmannians
Two compactifications of the space of holomorphic maps of fixed degree from a compact Riemann surface to a Grassmannian are studied. It is shown that the Uhlenbeck compactification has the structure of a projective variety and is dominated by the algebraic compactification coming from the Grothendieck Quot Scheme. The latter may be embedded into the moduli space of solutions to a generalized ve...
متن کاملGromov Hyperbolicity of Certain Conformal Invariant Metrics
The unit ball B is shown to be Gromov hyperbolic with respect to the Ferrand metric λBn and the modulus metric μBn , and dimension dependent upper bounds for the Gromov delta are obtained. In the two-dimensional case Gromov hyperbolicity is proved for all simply connected domains G. For λG also the case G = R n \ {0} is studied.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Mathematica Sinica, English Series
سال: 2006
ISSN: 1439-8516,1439-7617
DOI: 10.1007/s10114-005-0547-z