Metric Conformal Structures and Hyperbolic Dimension
نویسنده
چکیده
For any hyperbolic complex X and a ∈ X we construct a visual metric ď = ďa on ∂X that makes the Isom(X)-action on ∂X bi-Lipschitz, Möbius, symmetric and conformal. We define a stereographic projection of ďa and show that it is a metric conformally equivalent to ďa. We also introduce a notion of hyperbolic dimension for hyperbolic spaces with group actions. Problems related to hyperbolic dimension are discussed.
منابع مشابه
quaternionic contact structures in dimension 7
The conformal infinity of a quaternionic-Kähler metric on a 4n-manifold with boundary is a codimension 3-distribution on the boundary called quaternionic contact. In dimensions 4n− 1 greater than 7, a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension 7, we prove a criterion for quaternionic contact structures to be the...
متن کاملStructures in Dimension 7
The conformal infinity of a quaternionic-Kähler metric on a 4n-manifold with boundary is a codimension 3-distribution on the boundary called quaternionic contact. In dimensions 4n − 1 greater than 7, a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension 7, we prove a criterion for quaternionic contact structures to be th...
متن کاملConformal dimension and canonical splittings of hyperbolic groups
We prove a general criterion for a metric space to have conformal dimension one. The conditions are stated in terms of the existence of enough local cut points in the space. We then apply this criterion to the boundaries of hyperbolic groups and show an interesting relationship between conformal dimension and some canonical splittings of the group.
متن کاملSpaces with Conformal Dimension Greater than One
We show that if a complete, doubling metric space is annulus linearly connected then its conformal dimension is greater than one, quantitatively. As a consequence, hyperbolic groups whose boundaries have no local cut points have conformal dimension greater than one; this answers a question of Bonk and Kleiner.
متن کاملSpaces and Groups with Conformal Dimension Greater than One
We show that if a complete, doubling metric space is annularly linearly connected then its conformal dimension is greater than one, quantitatively. As a consequence, we answer a question of Bonk and Kleiner: if the boundary of a one-ended hyperbolic group has no local cut points, then its conformal dimension is greater than one.
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 2007