for a finitely generated kleinian group one knows[ I heard this much after i
left the area] that delta < 2 implies geometrically finite which implies the
result….see chris bishop et al…the analysis in the geometrically finite
case is in my papers ACTA…1980s without the finite generation it is very
false by direct and simple constructions in the classical book by R. Ford
“Automorphic Forms”
DennisSullivan (2016-12-27 19:51:46 -0800 -0800):
in my paper for kuipers 60 th birthday I produced a [socalled degenerate]
limit of quasi fuchsian groups which had a limit set of hausdorf dim two and
lebesgue measure zero , but positive hausdorf measure for a slightly bigger
gauge function with a heuristic argument that rr logloglogr worked…which i
recall was later proved by curt mcmullen.
Comments
No, cf. [mcmullen1999hausdorff] Theorem 3.5
for a finitely generated kleinian group one knows[ I heard this much after i left the area] that delta < 2 implies geometrically finite which implies the result….see chris bishop et al…the analysis in the geometrically finite case is in my papers ACTA…1980s without the finite generation it is very false by direct and simple constructions in the classical book by R. Ford “Automorphic Forms”
in my paper for kuipers 60 th birthday I produced a [socalled degenerate] limit of quasi fuchsian groups which had a limit set of hausdorf dim two and lebesgue measure zero , but positive hausdorf measure for a slightly bigger gauge function with a heuristic argument that rr logloglogr worked…which i recall was later proved by curt mcmullen.