$\pi$-convergence: The dynamics of isometries of Hadamard spaces on the boundary

$\pi$-convergence: The dynamics of isometries of Hadamard spaces on the boundary

Mon, 08/06/2009
14:15 		Eric Swenson (Brigham Young) Geometry and Analysis Seminar Add to calendar L3
$ \pi $-convergence: The dynamics of isometries of Hadamard spaces on the boundary
It a classical result from Kleinian groups that a discrete group, $ G $, of isometries of hyperbolic k-space $ \Bbb H^k $ will act on the boundary sphere, $ S^{k-1} $, of $ \Bbb H^k $ as a convergence group. That is: For every sequence of distinct isometries $ (g_i)\subset G $ there is a subsequence $ {g_i{_j}) $ and points $ n,p \in \S^{k-1} $ such that for $ x \in S^{k-1} -\{n\} $, $ g_i_{j}(x) \to p $ uniformly on compact subsets