- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:43
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
18
2002
3
Non-rectifiable limit sets of dimension one
Christopher
Bishop
SUNY at Stony Brook, STONY BROOK, UNITED STATES
Hausdorff dimension, quasi-Fuchsian groups, quasiconformal deformation, critical exponent, convex core
We construct quasiconformal deformations of convergence type Fuchsian groups such that the resulting limit set is a Jordan curve of Hausdorff dimension 1, but having tangents almost nowhere. It is known that no divergence type group has such a deformation. The main tools in this construction are (1) a characterization of tangent points in terms of Peter Jones' $\beta$'s, (2) a result of Stephen Semmes that gives a Carleson type condition on a Beltrami coefficient which implies rectifiability and (3) a construction of quasiconformal deformations of a surface which shrink a given geodesic and whose dilatations satisfy an exponential decay estimate away from the geodesic.
Functions of a complex variable
General
653
684
10.4171/RMI/331
http://www.ems-ph.org/doi/10.4171/RMI/331