Non-rectifiable limit sets of dimension one
- Autores: Christopher J. Bishop
- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 18, Nº 3, 2002, págs. 653-684
- Idioma: inglés
- DOI: 10.4171/rmi/331
- Títulos paralelos:
- Conjuntos límite no rectificables de dimensión uno.
- Enlaces
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Resumen
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.
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