Function theory on a q-analog of complex hyperbolic space

On a characterization of the complex hyperbolic space

Consider a compact Kähler manifold Mm with Ricci curvature lower bound RicM ≥ −2 (m + 1) . Assume that its universal cover M̃ has maximal bottom of spectrum λ1 ( M̃ ) = m2. Then we prove that M̃ is isometric to the complex hyperbolic space CH.

Local rigidity of discrete groups acting on complex hyperbolic space

The superrigidity theorem of Margulis, see Zimmer [17], classifies finite dimensional representations of lattices in semi-simple Lie groups of real rank strictly larger than 1. It is a fundamental problem to obtain the classification of finite dimensional representations of lattices in rank I semi-simple Lie groups. That this problem will be considerably harder than the previous one is suggeste...

J Rgensen's Inequality for Complex Hyperbolic Space

Groups Quasi-isometric to Complex Hyperbolic Space

We show that any finitely generated group quasi-isometric to complex hyperbolic space is a finite extension of a properly discontinuous, cocompact subgroup of the isometry group.

Scattering Theory for Radial Nonlinear Schrödinger Equations on Hyperbolic Space

We study the long time behavior of radial solutions to nonlinear Schrödinger equations on hyperbolic space. We show that the usual distinction between short range and long range nonlinearity is modified: the geometry of the hyperbolic space makes every power-like nonlinearity short range. The proofs rely on weighted Strichartz estimates, which imply Strichartz estimates for a broader family of ...