Quasiconformal conjugacy classes of parabolic isometries of complex hyperbolic space

Youngju Kim

Vol. 270 (2014), No. 1, 129–149

DOI: 10.2140/pjm.2014.270.129

Abstract

We investigate the quasiconformal conjugacy classes of parabolic isometries acting on complex hyperbolic space. Our main result is that a screw parabolic isometry cannot be quasiconformally conjugate to a translation. This implies that a cyclic group generated by a screw parabolic isometry is not quasiconformally stable in its deformation space.

Keywords

Heisenberg group, parabolic isometry, complex hyperbolic space, quasiconformal stability

Mathematical Subject Classification 2010

Primary: 20H10, 30C65

Secondary: 51M10, 22E40, 32G07

Milestones

Received: 27 March 2013

Revised: 24 November 2013

Accepted: 28 November 2013

Published: 2 August 2014