Non-rectifiable limit sets of dimension one.

Bishop, Christopher J.. "Non-rectifiable limit sets of dimension one.." Revista Matemática Iberoamericana 18.3 (2002): 653-684. <http://eudml.org/doc/39698>.

@article{Bishop2002,
abstract = {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.},
author = {Bishop, Christopher J.},
journal = {Revista Matemática Iberoamericana},
keywords = {Superficies Riemann; Dimensión de Hausdorff; Grupos fuchsianos; Aplicaciones cuasiconformes; Rectificación; Curvas},
language = {eng},
number = {3},
pages = {653-684},
title = {Non-rectifiable limit sets of dimension one.},
url = {http://eudml.org/doc/39698},
volume = {18},
year = {2002},
}

TY - JOUR
AU - Bishop, Christopher J.
TI - Non-rectifiable limit sets of dimension one.
JO - Revista Matemática Iberoamericana
PY - 2002
VL - 18
IS - 3
SP - 653
EP - 684
AB - 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.
LA - eng
KW - Superficies Riemann; Dimensión de Hausdorff; Grupos fuchsianos; Aplicaciones cuasiconformes; Rectificación; Curvas
UR - http://eudml.org/doc/39698
ER -