Non-rectifiable limit sets of dimension one
Bishop, Christopher J.
Rev. Mat. Iberoamericana, Tome 18 (2002) no. 1, p. 653-684 / Harvested from Project Euclid
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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.
Publié le : 2002-03-14
Classification:  Hausdorff dimension,  quasi-Fuchsian groups,  quasiconformal deformation,  critical exponent,  convex core,  30F60 
@article{1051544322,
     author = {Bishop, Christopher J.},
     title = {Non-rectifiable limit sets of dimension one},
     journal = {Rev. Mat. Iberoamericana},
     volume = {18},
     number = {1},
     year = {2002},
     pages = { 653-684},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1051544322}
}

Bishop, Christopher J. Non-rectifiable limit sets of dimension one. Rev. Mat. Iberoamericana, Tome 18 (2002) no. 1, pp.  653-684. http://gdmltest.u-ga.fr/item/1051544322/