Maximal Convergence Groups and Rank One Symmetric Spaces

Details Maximal Convergence Groups and Rank One Symmetric Spaces Maximal Convergence Groups and Rank One Symmetric Spaces

2004-10-22

arxiv.org/abs/math/0410500v2

Mathematics

Dynamical Systems

Journal of the Australian Mathematical Society, to appear

Scientific paper

We show that the group of conformal homeomorphisms of the boundary of a rank one symmetric space (except the hyperbolic plane) of noncompact type acts as a maximal convergence group. Moreover, we show that any family of uniformly quasiconformal homeomorphisms has the convergence property. Our theorems generalize results of Gehring and Martin in the real hyperbolic case for M\"obius groups. As a consequence, this shows that the maximal convergence subgroups of the group of self homeomorphisms of the $d$-sphere are not unique up to conjugacy. Finally, we discuss some implications of maximality.

Affiliated with

Also associated with

No associations

Rating

Maximal Convergence Groups and Rank One Symmetric Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Maximal Convergence Groups and Rank One Symmetric Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Maximal Convergence Groups and Rank One Symmetric Spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-485345