Título inglés |
Non-rectifiable limit sets of dimension one. |
Título español |
Conjuntos límite no rectificables de dimensión uno. |
Autor/es |
Bishop, Christopher J. |
Organización |
Dep. Math. SUNY at Stony Brook, Stony Brook (New York), Estados Unidos |
Revista |
0213-2230 |
Publicación |
2002, 18 (3): 653-684, 13 Ref. |
Tipo de documento |
articulo |
Idioma |
Inglés |
Resumen inglés |
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. |
Clasificación UNESCO |
120209 |
Palabras clave español |
Superficies Riemann ; Dimensión de Hausdorff ; Grupos fuchsianos ; Aplicaciones cuasiconformes ; Rectificación ; Curvas |
Código MathReviews |
MR1954867 |
Código Z-Math |
Zbl 1064.30046 |
Acceso al artículo completo |