Analyticity of Hausdorff dimension of limit sets of Kleinian groups. (English) Zbl 0890.30028

Anderson, James W.; Rocha, André C.

Ann. Acad. Sci. Fenn., Math. 22, No. 2, 349-364 (1997).

We show that the Hausdorff dimension of the limit set is a real analytic function on the deformation space of a certain class of convex co-compact Kleinian groups, which includes all convex co-compact function groups. This extends a result of Ruelle for quasifuchsian groups.

Reviewer: J.W.Anderson (Southampton)

MSC:

30F40

Kleinian groups (aspects of compact Riemann surfaces and uniformization)

Keywords:

Hausdorff dimension; limit set; co-compact Kleinian groups