We prove that an Ahlfors-regular set (with dimension one) E ⊂ Rn which verifies a βq-version of P. W. Jones' geometric lemma is included in an Ahlfors-regular curve Γ.
This theorem is due to G. David and S. Semmes, we give a more direct proof.
@article{urn:eudml:doc:41259, title = {Sous-ensembles de courbes Ahlfors-r\'eguli\`eres et nombres de Jones.}, journal = {Publicacions Matem\`atiques}, volume = {40}, year = {1996}, pages = {497-526}, mrnumber = {MR1425633}, zbl = {0933.28002}, language = {fr}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41259} }
Pajot, Hervé. Sous-ensembles de courbes Ahlfors-régulières et nombres de Jones.. Publicacions Matemàtiques, Tome 40 (1996) pp. 497-526. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41259/