Hyperbolic-type metrics
نویسنده
چکیده
The article is a status report on the contemporary research of hyperbolic-type metrics, and considers progress in the study of the classes of isometryand bilipschitz mappings with respect to some of the presented metrics. Also, the Gromov hyperbolicity question is discussed.
منابع مشابه
Families Index for Manifolds with Hyperbolic Cusp Singularities
Manifolds with fibered hyperbolic cusp metrics include hyperbolic manifolds with cusps and locally symmetric spaces of Q-rank one. We extend Vaillant’s treatment of Dirac-type operators associated to these metrics by weaking the hypotheses on the boundary families through the use of Fredholm perturbations as in the family index theorem of Melrose and Piazza and by treating the index of families...
متن کاملHyperbolic 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.
متن کاملLipschitz Type Characterizations for Bergman Spaces
We obtain new characterizations for Bergman spaces with standard weights in terms of Lipschitz type conditions in the Euclidean, hyperbolic, and pseudo-hyperbolic metrics. As a consequence, we prove optimal embedding theorems when an analytic function on the unit disk is symmetrically lifted to the bidisk.
متن کاملEquilibrium States for Lattice Models of Hyperbolic Type
We study the structural stability of coupled map lattice models of hyperbolic type under certain metrics. We prove the existence of equilibrium states for continuous functions on lattice models under the conditions of weak interaction and translation invariance. We also study the uniqueness and ergodic properties of these equilibrium states for HH older continuous functions.
متن کاملOn Length Spectrum Metrics and Weak Metrics on Teichmüller Spaces of Surfaces with Boundary
We define and study metrics and weak metrics on the Teichmüller space of a surface of topologically finite type with boundary. These metrics and weak metrics are associated to the hyperbolic length spectrum of simple closed curves and of properly embedded arcs in the surface. We give a comparison between the defined metrics on regions of Teichmüller space which we call ε0-relative ǫ-thick parts...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006