# Non-rectifiable limit sets of dimension one.

Revista Matemática Iberoamericana (2002)

- Volume: 18, Issue: 3, page 653-684
- ISSN: 0213-2230

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topBishop, 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 -

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