Event time:
Monday, September 29, 2008 - 12:30pm to 1:30pm
Location:
431 DL
Speaker:
Youngju Kim
Speaker affiliation:
City University of New York
Event description:
It is known that a geometrically finite Kleinian group is quasiconformally stable. We prove that this quasiconformal stability cannot be generalized in 4-dimensional hyperbolic space. This is due to the presence of screw parabolic isometries in dimension 4. We also prove that a Fuchsian thrice-punctured sphere group has a large deformation space in hyperbolic 4-space which is in contrast to lower imensions where the Fuchsian thrice-punctured sphere group has a trivial deformation space. However, the thrice-punctured
sphere group is still quasiconformally rigid.